2 added
2 removed
Original
2026-01-01
Modified
2026-02-28
1
-
<p>196 Learners</p>
1
+
<p>227 Learners</p>
2
<p>Last updated on<strong>August 5, 2025</strong></p>
2
<p>Last updated on<strong>August 5, 2025</strong></p>
3
<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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 352.</p>
3
<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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 352.</p>
4
<h2>What is the Square Root of 352?</h2>
4
<h2>What is the Square Root of 352?</h2>
5
<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 352 is not a<a>perfect square</a>. The square root of 352 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √352, whereas in exponential form it is expressed as (352)^(1/2). √352 ≈ 18.761, 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>
5
<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 352 is not a<a>perfect square</a>. The square root of 352 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √352, whereas in exponential form it is expressed as (352)^(1/2). √352 ≈ 18.761, 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 352</h2>
6
<h2>Finding the Square Root of 352</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 long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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 long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
8
<ul><li>Prime factorization method</li>
8
<ul><li>Prime factorization method</li>
9
<li>Long division method</li>
9
<li>Long division method</li>
10
<li>Approximation method</li>
10
<li>Approximation method</li>
11
</ul><h2>Square Root of 352 by Prime Factorization Method</h2>
11
</ul><h2>Square Root of 352 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 352 is broken down into its prime factors.</p>
12
<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 352 is broken down into its prime factors.</p>
13
<p><strong>Step 1:</strong>Finding the prime factors of 352 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 11:<a>2^5</a>x 11</p>
13
<p><strong>Step 1:</strong>Finding the prime factors of 352 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 11:<a>2^5</a>x 11</p>
14
<p><strong>Step 2:</strong>Now we have found the prime factors of 352. The second step is to make pairs of those prime factors. Since 352 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
14
<p><strong>Step 2:</strong>Now we have found the prime factors of 352. The second step is to make pairs of those prime factors. Since 352 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
15
<p>Therefore, calculating the<a>square root</a>of 352 using prime factorization is not straightforward.</p>
15
<p>Therefore, calculating the<a>square root</a>of 352 using prime factorization is not straightforward.</p>
16
<h3>Explore Our Programs</h3>
16
<h3>Explore Our Programs</h3>
17
-
<p>No Courses Available</p>
18
<h2>Square Root of 352 by Long Division Method</h2>
17
<h2>Square Root of 352 by Long Division Method</h2>
19
<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 square root using the long division method, step by step.</p>
18
<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 square root 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 352, we group it as 52 and 3.</p>
19
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 352, we group it as 52 and 3.</p>
21
<p><strong>Step 2:</strong>Now we need to find n whose square is 3. We can say n as ‘1’ because 1 x 1 is<a>less than</a>or equal to 3. Now the<a>quotient</a>is 1, and after subtracting 1, the<a>remainder</a>is 2.</p>
20
<p><strong>Step 2:</strong>Now we need to find n whose square is 3. We can say n as ‘1’ because 1 x 1 is<a>less than</a>or equal to 3. Now the<a>quotient</a>is 1, and after subtracting 1, the<a>remainder</a>is 2.</p>
22
<p><strong>Step 3:</strong>Now let us bring down 52 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>
21
<p><strong>Step 3:</strong>Now let us bring down 52 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>
23
<p><strong>Step 4:</strong>The new divisor will be 2n. We need to find the value of n such that 2n x n ≤ 252. Let’s consider n as 8, now 28 x 8 = 224.</p>
22
<p><strong>Step 4:</strong>The new divisor will be 2n. We need to find the value of n such that 2n x n ≤ 252. Let’s consider n as 8, now 28 x 8 = 224.</p>
24
<p><strong>Step 5:</strong>Subtract 224 from 252, the difference is 28, and the quotient is 18.</p>
23
<p><strong>Step 5:</strong>Subtract 224 from 252, the difference is 28, and the quotient is 18.</p>
25
<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 2800.</p>
24
<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 2800.</p>
26
<p><strong>Step 7:</strong>Now we need to find the new divisor that is 186 because 186 x 6 = 1116</p>
25
<p><strong>Step 7:</strong>Now we need to find the new divisor that is 186 because 186 x 6 = 1116</p>
27
<p><strong>Step 8:</strong>Subtracting 1116 from 2800, we get the result 1684.</p>
26
<p><strong>Step 8:</strong>Subtracting 1116 from 2800, we get the result 1684.</p>
28
<p><strong>Step 9:</strong>Now the quotient is 18.7</p>
27
<p><strong>Step 9:</strong>Now the quotient is 18.7</p>
29
<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values continue till the remainder is zero.</p>
28
<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values continue till the remainder is zero.</p>
30
<p>So the square root of √352 is approximately 18.76</p>
29
<p>So the square root of √352 is approximately 18.76</p>
31
<h2>Square Root of 352 by Approximation Method</h2>
30
<h2>Square Root of 352 by Approximation Method</h2>
32
<p>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 352 using the approximation method.</p>
31
<p>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 352 using the approximation method.</p>
33
<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √352.</p>
32
<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √352.</p>
34
<p>The smallest perfect square less than 352 is 324, and the largest perfect square<a>greater than</a>352 is 361. √352 falls somewhere between 18 and 19.</p>
33
<p>The smallest perfect square less than 352 is 324, and the largest perfect square<a>greater than</a>352 is 361. √352 falls somewhere between 18 and 19.</p>
35
<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (352 - 324) / (361 - 324) = 0.756.</p>
34
<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (352 - 324) / (361 - 324) = 0.756.</p>
36
<p>Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 18 + 0.756 = 18.756, so the square root of 352 is approximately 18.76.</p>
35
<p>Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 18 + 0.756 = 18.756, so the square root of 352 is approximately 18.76.</p>
37
<h2>Common Mistakes and How to Avoid Them in the Square Root of 352</h2>
36
<h2>Common Mistakes and How to Avoid Them in the Square Root of 352</h2>
38
<p>Students do make mistakes while finding square roots, such as forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes in detail.</p>
37
<p>Students do make mistakes while finding square roots, such as forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes in detail.</p>
38
+
<h2>Download Worksheets</h2>
39
<h3>Problem 1</h3>
39
<h3>Problem 1</h3>
40
<p>Can you help Max find the area of a square box if its side length is given as √352?</p>
40
<p>Can you help Max find the area of a square box if its side length is given as √352?</p>
41
<p>Okay, lets begin</p>
41
<p>Okay, lets begin</p>
42
<p>The area of the square is approximately 124.56 square units.</p>
42
<p>The area of the square is approximately 124.56 square units.</p>
43
<h3>Explanation</h3>
43
<h3>Explanation</h3>
44
<p>The area of the square = side^2.</p>
44
<p>The area of the square = side^2.</p>
45
<p>The side length is given as √352.</p>
45
<p>The side length is given as √352.</p>
46
<p>Area of the square = side^2 = √352 x √352 = 18.76 × 18.76 ≈ 352</p>
46
<p>Area of the square = side^2 = √352 x √352 = 18.76 × 18.76 ≈ 352</p>
47
<p>Therefore, the area of the square box is approximately 352 square units.</p>
47
<p>Therefore, the area of the square box is approximately 352 square units.</p>
48
<p>Well explained 👍</p>
48
<p>Well explained 👍</p>
49
<h3>Problem 2</h3>
49
<h3>Problem 2</h3>
50
<p>A square-shaped building measuring 352 square feet is built; if each of the sides is √352, what will be the square feet of half of the building?</p>
50
<p>A square-shaped building measuring 352 square feet is built; if each of the sides is √352, what will be the square feet of half of the building?</p>
51
<p>Okay, lets begin</p>
51
<p>Okay, lets begin</p>
52
<p>176 square feet</p>
52
<p>176 square feet</p>
53
<h3>Explanation</h3>
53
<h3>Explanation</h3>
54
<p>We can just divide the given area by 2 as the building is square-shaped.</p>
54
<p>We can just divide the given area by 2 as the building is square-shaped.</p>
55
<p>Dividing 352 by 2 = 176 So half of the building measures 176 square feet.</p>
55
<p>Dividing 352 by 2 = 176 So half of the building measures 176 square feet.</p>
56
<p>Well explained 👍</p>
56
<p>Well explained 👍</p>
57
<h3>Problem 3</h3>
57
<h3>Problem 3</h3>
58
<p>Calculate √352 x 5.</p>
58
<p>Calculate √352 x 5.</p>
59
<p>Okay, lets begin</p>
59
<p>Okay, lets begin</p>
60
<p>93.8</p>
60
<p>93.8</p>
61
<h3>Explanation</h3>
61
<h3>Explanation</h3>
62
<p>The first step is to find the square root of 352 which is approximately 18.76, the second step is to multiply 18.76 with 5. So 18.76 x 5 ≈ 93.8</p>
62
<p>The first step is to find the square root of 352 which is approximately 18.76, the second step is to multiply 18.76 with 5. So 18.76 x 5 ≈ 93.8</p>
63
<p>Well explained 👍</p>
63
<p>Well explained 👍</p>
64
<h3>Problem 4</h3>
64
<h3>Problem 4</h3>
65
<p>What will be the square root of (352 + 100)?</p>
65
<p>What will be the square root of (352 + 100)?</p>
66
<p>Okay, lets begin</p>
66
<p>Okay, lets begin</p>
67
<p>The square root is 20.</p>
67
<p>The square root is 20.</p>
68
<h3>Explanation</h3>
68
<h3>Explanation</h3>
69
<p>To find the square root, we need to find the sum of (352 + 100). 352 + 100 = 452, and then √452 ≈ 21.26.</p>
69
<p>To find the square root, we need to find the sum of (352 + 100). 352 + 100 = 452, and then √452 ≈ 21.26.</p>
70
<p>Therefore, the square root of (352 + 100) is approximately ±21.26.</p>
70
<p>Therefore, the square root of (352 + 100) is approximately ±21.26.</p>
71
<p>Well explained 👍</p>
71
<p>Well explained 👍</p>
72
<h3>Problem 5</h3>
72
<h3>Problem 5</h3>
73
<p>Find the perimeter of the rectangle if its length ‘l’ is √352 units and the width ‘w’ is 38 units.</p>
73
<p>Find the perimeter of the rectangle if its length ‘l’ is √352 units and the width ‘w’ is 38 units.</p>
74
<p>Okay, lets begin</p>
74
<p>Okay, lets begin</p>
75
<p>The perimeter of the rectangle is approximately 113.52 units.</p>
75
<p>The perimeter of the rectangle is approximately 113.52 units.</p>
76
<h3>Explanation</h3>
76
<h3>Explanation</h3>
77
<p>Perimeter of the rectangle = 2 × (length + width).</p>
77
<p>Perimeter of the rectangle = 2 × (length + width).</p>
78
<p>Perimeter = 2 × (√352 + 38) = 2 × (18.76 + 38) = 2 × 56.76 ≈ 113.52 units.</p>
78
<p>Perimeter = 2 × (√352 + 38) = 2 × (18.76 + 38) = 2 × 56.76 ≈ 113.52 units.</p>
79
<p>Well explained 👍</p>
79
<p>Well explained 👍</p>
80
<h2>FAQ on Square Root of 352</h2>
80
<h2>FAQ on Square Root of 352</h2>
81
<h3>1.What is √352 in its simplest form?</h3>
81
<h3>1.What is √352 in its simplest form?</h3>
82
<p>The prime factorization of 352 is 2 x 2 x 2 x 2 x 2 x 11, so the simplest form of √352 = √(2^5 x 11).</p>
82
<p>The prime factorization of 352 is 2 x 2 x 2 x 2 x 2 x 11, so the simplest form of √352 = √(2^5 x 11).</p>
83
<h3>2.Mention the factors of 352.</h3>
83
<h3>2.Mention the factors of 352.</h3>
84
<p>Factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, and 352.</p>
84
<p>Factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, and 352.</p>
85
<h3>3.Calculate the square of 352.</h3>
85
<h3>3.Calculate the square of 352.</h3>
86
<p>We get the square of 352 by multiplying the number by itself, that is 352 x 352 = 123,904.</p>
86
<p>We get the square of 352 by multiplying the number by itself, that is 352 x 352 = 123,904.</p>
87
<h3>4.Is 352 a prime number?</h3>
87
<h3>4.Is 352 a prime number?</h3>
88
<h3>5.352 is divisible by?</h3>
88
<h3>5.352 is divisible by?</h3>
89
<p>352 has many factors; those are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, and 352.</p>
89
<p>352 has many factors; those are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, and 352.</p>
90
<h2>Important Glossaries for the Square Root of 352</h2>
90
<h2>Important Glossaries for the Square Root of 352</h2>
91
<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>
91
<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>
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>
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, it is always the positive square root that has more prominence due to its uses in the real world. That is why it is also known as the principal square root.</li>
93
</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is why it is also known as the principal square root.</li>
94
</ul><ul><li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.</li>
94
</ul><ul><li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.</li>
95
</ul><ul><li><strong>Prime factorization:</strong>The expression of a number as the product of its prime factors. For example, the prime factorization of 352 is 2^5 x 11.</li>
95
</ul><ul><li><strong>Prime factorization:</strong>The expression of a number as the product of its prime factors. For example, the prime factorization of 352 is 2^5 x 11.</li>
96
</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
96
</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
97
<p>▶</p>
97
<p>▶</p>
98
<h2>Jaskaran Singh Saluja</h2>
98
<h2>Jaskaran Singh Saluja</h2>
99
<h3>About the Author</h3>
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>
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>
101
<h3>Fun Fact</h3>
102
<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
102
<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>