1 added
91 removed
Original
2026-01-01
Modified
2026-02-28
1
-
<p>186 Learners</p>
2
-
<p>Last updated on<strong>August 5, 2025</strong></p>
3
-
<p>If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 734.</p>
4
-
<h2>What is the Square Root of 734?</h2>
5
-
<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 734 is not a<a>perfect square</a>. The square root of 734 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √734, whereas in exponential form it is (734)^(1/2). √734 ≈ 27.086, 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>
6
-
<h2>Finding the Square Root of 734</h2>
7
-
<p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where<a>long division</a>and approximation methods are used. Let us now learn the following methods:</p>
8
-
<ul><li>Prime factorization method</li>
9
-
<li>Long division method</li>
10
-
<li>Approximation method</li>
11
-
</ul><h2>Square Root of 734 by Prime Factorization Method</h2>
12
-
<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 734 is broken down into its prime factors:</p>
13
-
<p><strong>Step 1</strong>: Finding the prime factors of 734</p>
14
-
<p>Breaking it down, we get 2 x 367: 2^1 x 367^1</p>
15
-
<p><strong>Step 2:</strong>Now we found out the prime factors of 734. The second step is to make pairs of those prime factors. Since 734 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 734 using prime factorization is not straightforward.</p>
16
-
<h3>Explore Our Programs</h3>
17
-
<p>No Courses Available</p>
18
-
<h2>Square Root of 734 by Long Division Method</h2>
19
<p>The long<a>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>
1
<p>The long<a>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>
20
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 734, we need to group it as 34 and 7.</p>
2
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 734, we need to group it as 34 and 7.</p>
21
<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 7. We can say n is ‘2’ because 2 × 2 = 4, which is less than 7. Now the<a>quotient</a>is 2. After subtracting 4 from 7, the<a>remainder</a>is 3.</p>
3
<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 7. We can say n is ‘2’ because 2 × 2 = 4, which is less than 7. Now the<a>quotient</a>is 2. After subtracting 4 from 7, the<a>remainder</a>is 3.</p>
22
<p><strong>Step 3:</strong>Now bring down 34, making the new<a>dividend</a>334. Add the old<a>divisor</a>with the same number: 2 + 2 = 4, which will be our new divisor.</p>
4
<p><strong>Step 3:</strong>Now bring down 34, making the new<a>dividend</a>334. Add the old<a>divisor</a>with the same number: 2 + 2 = 4, which will be our new divisor.</p>
23
<p><strong>Step 4:</strong>The new divisor will be 4n. We need to find the value of n.</p>
5
<p><strong>Step 4:</strong>The new divisor will be 4n. We need to find the value of n.</p>
24
<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 334. Let us consider n as 7, now 4 × 7 × 7 = 329.</p>
6
<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 334. Let us consider n as 7, now 4 × 7 × 7 = 329.</p>
25
<p><strong>Step 6:</strong>Subtract 329 from 334, the difference is 5, and the quotient is 27.</p>
7
<p><strong>Step 6:</strong>Subtract 329 from 334, the difference is 5, and the quotient is 27.</p>
26
<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 zeros to the dividend. Now the new dividend is 500.</p>
8
<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 zeros to the dividend. Now the new dividend is 500.</p>
27
<p><strong>Step 8:</strong>Now we need to find the new divisor that is 541 because 541 × 1 = 541.</p>
9
<p><strong>Step 8:</strong>Now we need to find the new divisor that is 541 because 541 × 1 = 541.</p>
28
<p><strong>Step 9:</strong>Subtracting 541 from 500 is not possible, so consider 27.0 and continue the process until you have two decimal places.</p>
10
<p><strong>Step 9:</strong>Subtracting 541 from 500 is not possible, so consider 27.0 and continue the process until you have two decimal places.</p>
29
<p>The square root of √734 is approximately 27.086.</p>
11
<p>The square root of √734 is approximately 27.086.</p>
30
-
<h2>Square Root of 734 by Approximation Method</h2>
12
+
31
-
<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 734 using the approximation method.</p>
32
-
<p><strong>Step 1:</strong>Now we have to find the closest perfect squares to √734. The smallest perfect square less than 734 is 729, and the largest perfect square<a>greater than</a>734 is 784. √734 falls somewhere between 27 and 28.</p>
33
-
<p><strong>Step 2</strong>: Now apply the<a>formula</a>: Given number - smallest perfect square / (Greater perfect square - smallest perfect square) Going by the formula (734 - 729) ÷ (784 - 729) ≈ 0.086. Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number: 27 + 0.086 ≈ 27.086. So, the square root of 734 is approximately 27.086.</p>
34
-
<h2>Common Mistakes and How to Avoid Them in the Square Root of 734</h2>
35
-
<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root and skipping long division steps. Let's look at a few mistakes students tend to make in detail.</p>
36
-
<h3>Problem 1</h3>
37
-
<p>Can you help Max find the area of a square box if its side length is given as √734?</p>
38
-
<p>Okay, lets begin</p>
39
-
<p>The area of the square is approximately 538.324 square units.</p>
40
-
<h3>Explanation</h3>
41
-
<p>The area of the square = side^2.</p>
42
-
<p>The side length is given as √734.</p>
43
-
<p>Area of the square = side^2 = √734 × √734 ≈ 27.086 × 27.086 ≈ 734</p>
44
-
<p>Therefore, the area of the square box is approximately 538.324 square units.</p>
45
-
<p>Well explained 👍</p>
46
-
<h3>Problem 2</h3>
47
-
<p>A square-shaped building measuring 734 square feet is built; if each of the sides is √734, what will be the square feet of half of the building?</p>
48
-
<p>Okay, lets begin</p>
49
-
<p>367 square feet</p>
50
-
<h3>Explanation</h3>
51
-
<p>We can just divide the given area by 2 as the building is square-shaped.</p>
52
-
<p>Dividing 734 by 2, we get 367.</p>
53
-
<p>So half of the building measures 367 square feet.</p>
54
-
<p>Well explained 👍</p>
55
-
<h3>Problem 3</h3>
56
-
<p>Calculate √734 × 5.</p>
57
-
<p>Okay, lets begin</p>
58
-
<p>Approximately 135.43</p>
59
-
<h3>Explanation</h3>
60
-
<p>The first step is to find the square root of 734, which is approximately 27.086.</p>
61
-
<p>The second step is to multiply 27.086 by 5.</p>
62
-
<p>So 27.086 × 5 ≈ 135.43</p>
63
-
<p>Well explained 👍</p>
64
-
<h3>Problem 4</h3>
65
-
<p>What will be the square root of (734 + 6)?</p>
66
-
<p>Okay, lets begin</p>
67
-
<p>The square root is approximately 24.58</p>
68
-
<h3>Explanation</h3>
69
-
<p>To find the square root, we need to find the sum of (734 + 6). 734 + 6 = 740, and then √740 ≈ 27.195.</p>
70
-
<p>Therefore, the square root of (734 + 6) is approximately 27.195.</p>
71
-
<p>Well explained 👍</p>
72
-
<h3>Problem 5</h3>
73
-
<p>Find the perimeter of the rectangle if its length ‘l’ is √734 units and the width ‘w’ is 38 units.</p>
74
-
<p>Okay, lets begin</p>
75
-
<p>The perimeter of the rectangle is approximately 130.172 units.</p>
76
-
<h3>Explanation</h3>
77
-
<p>Perimeter of the rectangle = 2 × (length + width).</p>
78
-
<p>Perimeter = 2 × (√734 + 38) ≈ 2 × (27.086 + 38) ≈ 2 × 65.086 ≈ 130.172 units.</p>
79
-
<p>Well explained 👍</p>
80
-
<h2>FAQ on Square Root of 734</h2>
81
-
<h3>1.What is √734 in its simplest form?</h3>
82
-
<p>The prime factorization of 734 is 2 x 367, so the simplest form of √734 = √(2 x 367).</p>
83
-
<h3>2.Mention the factors of 734.</h3>
84
-
<p>Factors of 734 are 1, 2, 367, and 734.</p>
85
-
<h3>3.Calculate the square of 734.</h3>
86
-
<p>We get the square of 734 by multiplying the number by itself, that is 734 × 734 = 538756.</p>
87
-
<h3>4.Is 734 a prime number?</h3>
88
-
<h3>5.734 is divisible by?</h3>
89
-
<p>734 is divisible by 1, 2, 367, and 734.</p>
90
-
<h2>Important Glossaries for the Square Root of 734</h2>
91
-
<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 4^2 = 16, and the inverse of the square is the square root, which is √16 = 4.</li>
92
-
</ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.</li>
93
-
</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, the positive square root is often used more in real-world applications. This is known as the principal square root.</li>
94
-
</ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because it is 4^2.</li>
95
-
</ul><ul><li><strong>Prime factorization:</strong>Prime factorization is the process of expressing a number as the product of prime numbers.</li>
96
-
</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
97
-
<p>▶</p>
98
-
<h2>Jaskaran Singh Saluja</h2>
99
-
<h3>About the Author</h3>
100
-
<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>
101
-
<h3>Fun Fact</h3>
102
-
<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>