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2026-01-01
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2026-02-28
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<p>213 Learners</p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 334.</p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 334.</p>
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<h2>What is the Square Root of 334?</h2>
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<h2>What is the Square Root of 334?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 334 is not a<a>perfect square</a>. The square root of 334 is expressed in both radical and exponential forms. In the radical form, it is expressed as √334, whereas in<a>exponential form</a>it is (334)^(1/2). √334 ≈ 18.276, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 334 is not a<a>perfect square</a>. The square root of 334 is expressed in both radical and exponential forms. In the radical form, it is expressed as √334, whereas in<a>exponential form</a>it is (334)^(1/2). √334 ≈ 18.276, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<h2>Finding the Square Root of 334</h2>
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<h2>Finding the Square Root of 334</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is typically not used; instead, the long-<a>division</a>method and approximation method are used. Let us now learn the following methods: - Prime factorization method - Long division method - Approximation method</p>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is typically not used; instead, the long-<a>division</a>method and approximation method are used. Let us now learn the following methods: - Prime factorization method - Long division method - Approximation method</p>
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<h2>Square Root of 334 by Prime Factorization Method</h2>
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<h2>Square Root of 334 by Prime Factorization Method</h2>
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<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 334 is broken down into its prime factors:</p>
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<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 334 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 334 Breaking it down, we get 2 x 167: 2^1 x 167^1</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 334 Breaking it down, we get 2 x 167: 2^1 x 167^1</p>
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<p><strong>Step 2:</strong>We found the prime factors of 334. The second step is to make pairs of those prime factors. Since 334 is not a perfect square, the digits of the number cannot be grouped in pairs.</p>
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<p><strong>Step 2:</strong>We found the prime factors of 334. The second step is to make pairs of those prime factors. Since 334 is not a perfect square, the digits of the number cannot be grouped in pairs.</p>
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<p>Therefore, calculating 334 using prime factorization alone is not possible.</p>
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<p>Therefore, calculating 334 using prime factorization alone is not possible.</p>
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<h2>Square Root of 334 by Long Division Method</h2>
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<h2>Square Root of 334 by Long Division Method</h2>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step:</p>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step:</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 334, we need to group it as 34 and 3.</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 334, we need to group it as 34 and 3.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 3. We can say n is ‘1’ because 1 x 1 is<a>less than</a>or equal to 3. Now the<a>quotient</a>is 1. After subtracting 1 from 3, the<a>remainder</a>is 2.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 3. We can say n is ‘1’ because 1 x 1 is<a>less than</a>or equal to 3. Now the<a>quotient</a>is 1. After subtracting 1 from 3, the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 34, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1 to get 2, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 34, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1 to get 2, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 234. Let us consider n as 9, now 2 x 9 x 9 = 162.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 234. Let us consider n as 9, now 2 x 9 x 9 = 162.</p>
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<p><strong>Step 6:</strong>Subtracting 162 from 234 gives the difference of 72, and the quotient is 19.</p>
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<p><strong>Step 6:</strong>Subtracting 162 from 234 gives the difference of 72, and the quotient is 19.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 7200.</p>
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<p><strong>Step 7:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 7200.</p>
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<p><strong>Step 8:</strong>Now we need to find a new divisor.</p>
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<p><strong>Step 8:</strong>Now we need to find a new divisor.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.</p>
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<p>So the square root of √334 ≈ 18.276</p>
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<p>So the square root of √334 ≈ 18.276</p>
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<h2>Square Root of 334 by Approximation Method</h2>
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<h2>Square Root of 334 by Approximation Method</h2>
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<p>The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 334 using the approximation method.</p>
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<p>The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 334 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √334.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √334.</p>
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<p>The smallest perfect square less than 334 is 324, and the largest perfect square<a>greater than</a>334 is 361. √334 falls somewhere between 18 and 19.</p>
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<p>The smallest perfect square less than 334 is 324, and the largest perfect square<a>greater than</a>334 is 361. √334 falls somewhere between 18 and 19.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)</p>
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<p>Using the formula, (334 - 324) / (361 - 324) = 10 / 37 ≈ 0.27 Adding this value to the lower perfect square root: 18 + 0.27 = 18.27</p>
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<p>Using the formula, (334 - 324) / (361 - 324) = 10 / 37 ≈ 0.27 Adding this value to the lower perfect square root: 18 + 0.27 = 18.27</p>
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<p>Therefore, the approximate square root of 334 is 18.27</p>
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<p>Therefore, the approximate square root of 334 is 18.27</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 334</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 334</h2>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these mistakes in detail.</p>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these mistakes in detail.</p>
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<h2>Download Worksheets</h2>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Can you help Max find the area of a square box if its side length is given as √334?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √334?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 334 square units.</p>
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<p>The area of the square is approximately 334 square units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The area of the square = side².</p>
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<p>The area of the square = side².</p>
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<p>The side length is given as √334.</p>
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<p>The side length is given as √334.</p>
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<p>Area of the square = side² = √334 x √334 ≈ 334 square units.</p>
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<p>Area of the square = side² = √334 x √334 ≈ 334 square units.</p>
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<p>Therefore, the area of the square box is approximately 334 square units.</p>
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<p>Therefore, the area of the square box is approximately 334 square units.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>A square-shaped building measuring 334 square feet is built; if each of the sides is √334, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 334 square feet is built; if each of the sides is √334, what will be the square feet of half of the building?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>167 square feet</p>
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<p>167 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We can simply divide the given area by 2 as the building is square-shaped.</p>
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<p>We can simply divide the given area by 2 as the building is square-shaped.</p>
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<p>Dividing 334 by 2 gives us 167.</p>
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<p>Dividing 334 by 2 gives us 167.</p>
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<p>So half of the building measures 167 square feet.</p>
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<p>So half of the building measures 167 square feet.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>Calculate √334 x 5.</p>
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<p>Calculate √334 x 5.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Approximately 91.38</p>
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<p>Approximately 91.38</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 334, which is approximately 18.276.</p>
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<p>The first step is to find the square root of 334, which is approximately 18.276.</p>
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<p>The second step is to multiply 18.276 by 5.</p>
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<p>The second step is to multiply 18.276 by 5.</p>
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<p>Therefore, 18.276 x 5 ≈ 91.38</p>
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<p>Therefore, 18.276 x 5 ≈ 91.38</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>What will be the square root of (334 + 6)?</p>
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<p>What will be the square root of (334 + 6)?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 19.</p>
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<p>The square root is approximately 19.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the square root, we need to find the sum of (334 + 6). 334 + 6 = 340, and then √340 ≈ 18.44.</p>
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<p>To find the square root, we need to find the sum of (334 + 6). 334 + 6 = 340, and then √340 ≈ 18.44.</p>
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<p>Therefore, the square root of (334 + 6) is approximately ±18.44</p>
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<p>Therefore, the square root of (334 + 6) is approximately ±18.44</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √334 units and the width ‘w’ is 38 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √334 units and the width ‘w’ is 38 units.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>We find the perimeter of the rectangle as approximately 112.552 units.</p>
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<p>We find the perimeter of the rectangle as approximately 112.552 units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Perimeter of the rectangle = 2 × (length + width)</p>
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<p>Perimeter of the rectangle = 2 × (length + width)</p>
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<p>Perimeter = 2 × (√334 + 38) = 2 × (18.276 + 38) ≈ 2 × 56.276 = 112.552 units.</p>
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<p>Perimeter = 2 × (√334 + 38) = 2 × (18.276 + 38) ≈ 2 × 56.276 = 112.552 units.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 334</h2>
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<h2>FAQ on Square Root of 334</h2>
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<h3>1.What is √334 in its simplest form?</h3>
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<h3>1.What is √334 in its simplest form?</h3>
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<p>The prime factorization of 334 is 2 x 167, so the simplest form of √334 is √(2 x 167).</p>
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<p>The prime factorization of 334 is 2 x 167, so the simplest form of √334 is √(2 x 167).</p>
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<h3>2.Mention the factors of 334.</h3>
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<h3>2.Mention the factors of 334.</h3>
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<p>Factors of 334 are 1, 2, 167, and 334.</p>
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<p>Factors of 334 are 1, 2, 167, and 334.</p>
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<h3>3.Calculate the square of 334.</h3>
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<h3>3.Calculate the square of 334.</h3>
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<p>We get the square of 334 by multiplying the number by itself, which is 334 x 334 = 111,556.</p>
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<p>We get the square of 334 by multiplying the number by itself, which is 334 x 334 = 111,556.</p>
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<h3>4.Is 334 a prime number?</h3>
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<h3>4.Is 334 a prime number?</h3>
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<h3>5.334 is divisible by?</h3>
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<h3>5.334 is divisible by?</h3>
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<p>334 has factors including 1, 2, 167, and 334 itself, so it is divisible by these numbers.</p>
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<p>334 has factors including 1, 2, 167, and 334 itself, so it is divisible by these numbers.</p>
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<h2>Important Glossaries for the Square Root of 334</h2>
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<h2>Important Glossaries for the Square Root of 334</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root, that is √16 = 4.</li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root, that is √16 = 4.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be expressed as a fraction p/q, where q is not equal to zero and p and q are integers.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be expressed as a fraction p/q, where q is not equal to zero and p and q are integers.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots, but the principal square root is the non-negative square root that is typically more useful in real-world applications.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots, but the principal square root is the non-negative square root that is typically more useful in real-world applications.</li>
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</ul><ul><li><strong>Prime factorization:</strong>This is the process of expressing a number as the product of its prime factors.</li>
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</ul><ul><li><strong>Prime factorization:</strong>This is the process of expressing a number as the product of its prime factors.</li>
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</ul><ul><li><strong>Approximation method:</strong>A method used to find the approximate value of the square root of a non-perfect square by estimating between two perfect squares.</li>
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</ul><ul><li><strong>Approximation method:</strong>A method used to find the approximate value of the square root of a non-perfect square by estimating between two perfect squares.</li>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<h2>Jaskaran Singh Saluja</h2>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>