2 added
2 removed
Original
2026-01-01
Modified
2026-02-21
1
-
<p>290 Learners</p>
1
+
<p>337 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 various fields such as vehicle design and finance. Here, we will discuss the square root of 10400.</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 various fields such as vehicle design and finance. Here, we will discuss the square root of 10400.</p>
4
<h2>What is the Square Root of 10400?</h2>
4
<h2>What is the Square Root of 10400?</h2>
5
<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 10400 is not a<a>perfect square</a>. The square root of 10400 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √10400, whereas it is expressed as (10400)^(1/2) in exponential form. √10400 = 102, which is a<a>rational number</a>because it can 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>. 10400 is not a<a>perfect square</a>. The square root of 10400 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √10400, whereas it is expressed as (10400)^(1/2) in exponential form. √10400 = 102, which is a<a>rational number</a>because it can 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 10400</h2>
6
<h2>Finding the Square Root of 10400</h2>
7
<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the 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, for non-perfect square numbers, the 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 10400 by Prime Factorization Method</h2>
11
</ul><h2>Square Root of 10400 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 10400 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 10400 is broken down into its prime factors.</p>
13
<p><strong>Step 1:</strong>Finding the prime factors of 10400.</p>
13
<p><strong>Step 1:</strong>Finding the prime factors of 10400.</p>
14
<p>Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 5 x 13 x 20: 2^4 x 5^2 x 13 x 20.</p>
14
<p>Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 5 x 13 x 20: 2^4 x 5^2 x 13 x 20.</p>
15
<p><strong>Step 2:</strong>Now we found out the prime factors of 10400. The second step is to make pairs of those prime factors. Since 10400 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating √10400 using prime factorization is possible.</p>
15
<p><strong>Step 2:</strong>Now we found out the prime factors of 10400. The second step is to make pairs of those prime factors. Since 10400 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating √10400 using prime factorization is possible.</p>
16
<h3>Explore Our Programs</h3>
16
<h3>Explore Our Programs</h3>
17
-
<p>No Courses Available</p>
18
<h2>Square Root of 10400 by Long Division Method</h2>
17
<h2>Square Root of 10400 by Long Division Method</h2>
19
<p>The<a>long division</a>method is particularly used for non-perfect square numbers, but it can also be used for perfect squares. 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>
18
<p>The<a>long division</a>method is particularly used for non-perfect square numbers, but it can also be used for perfect squares. 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 10400, we need to group it as 400 and 104.</p>
19
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 10400, we need to group it as 400 and 104.</p>
21
<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 104. We can say n is ‘10’ because 10 x 10 is<a>less than</a>or equal to 104. Now the<a>quotient</a>is 10, and after subtracting 100 from 104, the<a>remainder</a>is 4.</p>
20
<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 104. We can say n is ‘10’ because 10 x 10 is<a>less than</a>or equal to 104. Now the<a>quotient</a>is 10, and after subtracting 100 from 104, the<a>remainder</a>is 4.</p>
22
<p><strong>Step 3:</strong>Now let us bring down 00, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 10 + 10 to get 20, which will be our new divisor.</p>
21
<p><strong>Step 3:</strong>Now let us bring down 00, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 10 + 10 to get 20, which will be our new divisor.</p>
23
<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 20n as the new divisor, and we need to find the value of n.</p>
22
<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 20n as the new divisor, and we need to find the value of n.</p>
24
<p><strong>Step 5:</strong>The next step is finding 20n × n ≤ 400. Let us consider n as 2; now 20 x 2 x 2 = 400.</p>
23
<p><strong>Step 5:</strong>The next step is finding 20n × n ≤ 400. Let us consider n as 2; now 20 x 2 x 2 = 400.</p>
25
<p><strong>Step 6:</strong>Subtract 400 from 400, and the difference is 0.</p>
24
<p><strong>Step 6:</strong>Subtract 400 from 400, and the difference is 0.</p>
26
<p><strong>Step 7:</strong>Since the remainder is zero, the quotient is 102.</p>
25
<p><strong>Step 7:</strong>Since the remainder is zero, the quotient is 102.</p>
27
<p>So the square root of √10400 is 102.</p>
26
<p>So the square root of √10400 is 102.</p>
28
<h2>Square Root of 10400 by Approximation Method</h2>
27
<h2>Square Root of 10400 by Approximation Method</h2>
29
<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 10400 using the approximation method.</p>
28
<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 10400 using the approximation method.</p>
30
<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √10400. The smallest perfect square less than 10400 is 10000, and the largest perfect square<a>greater than</a>10400 is 10404. √10400 falls somewhere between 100 and 102.</p>
29
<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √10400. The smallest perfect square less than 10400 is 10000, and the largest perfect square<a>greater than</a>10400 is 10404. √10400 falls somewhere between 100 and 102.</p>
31
<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). Going by the formula (10400 - 10000) ÷ (10404 - 10000) = 100/404 = 0.25</p>
30
<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). Going by the formula (10400 - 10000) ÷ (10404 - 10000) = 100/404 = 0.25</p>
32
<p>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, which is 100 + 0.25 = 102.5, so the square root of 10400 is approximately 102.</p>
31
<p>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, which is 100 + 0.25 = 102.5, so the square root of 10400 is approximately 102.</p>
33
<h2>Common Mistakes and How to Avoid Them in the Square Root of 10400</h2>
32
<h2>Common Mistakes and How to Avoid Them in the Square Root of 10400</h2>
34
<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>
33
<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>
34
+
<h2>Download Worksheets</h2>
35
<h3>Problem 1</h3>
35
<h3>Problem 1</h3>
36
<p>Can you help Max find the area of a square box if its side length is given as √10400?</p>
36
<p>Can you help Max find the area of a square box if its side length is given as √10400?</p>
37
<p>Okay, lets begin</p>
37
<p>Okay, lets begin</p>
38
<p>The area of the square is 10400 square units.</p>
38
<p>The area of the square is 10400 square units.</p>
39
<h3>Explanation</h3>
39
<h3>Explanation</h3>
40
<p>The area of the square = side².</p>
40
<p>The area of the square = side².</p>
41
<p>The side length is given as √10400.</p>
41
<p>The side length is given as √10400.</p>
42
<p>Area of the square = side² = √10400 x √10400 = 102 x 102 = 10400.</p>
42
<p>Area of the square = side² = √10400 x √10400 = 102 x 102 = 10400.</p>
43
<p>Therefore, the area of the square box is 10400 square units.</p>
43
<p>Therefore, the area of the square box is 10400 square units.</p>
44
<p>Well explained 👍</p>
44
<p>Well explained 👍</p>
45
<h3>Problem 2</h3>
45
<h3>Problem 2</h3>
46
<p>A square-shaped building measuring 10400 square feet is built; if each of the sides is √10400, what will be the square feet of half of the building?</p>
46
<p>A square-shaped building measuring 10400 square feet is built; if each of the sides is √10400, what will be the square feet of half of the building?</p>
47
<p>Okay, lets begin</p>
47
<p>Okay, lets begin</p>
48
<p>5200 square feet.</p>
48
<p>5200 square feet.</p>
49
<h3>Explanation</h3>
49
<h3>Explanation</h3>
50
<p>We can just divide the given area by 2 as the building is square-shaped.</p>
50
<p>We can just divide the given area by 2 as the building is square-shaped.</p>
51
<p>Dividing 10400 by 2 gives us 5200.</p>
51
<p>Dividing 10400 by 2 gives us 5200.</p>
52
<p>So half of the building measures 5200 square feet.</p>
52
<p>So half of the building measures 5200 square feet.</p>
53
<p>Well explained 👍</p>
53
<p>Well explained 👍</p>
54
<h3>Problem 3</h3>
54
<h3>Problem 3</h3>
55
<p>Calculate √10400 x 5.</p>
55
<p>Calculate √10400 x 5.</p>
56
<p>Okay, lets begin</p>
56
<p>Okay, lets begin</p>
57
<p>510.</p>
57
<p>510.</p>
58
<h3>Explanation</h3>
58
<h3>Explanation</h3>
59
<p>The first step is to find the square root of 10400, which is 102.</p>
59
<p>The first step is to find the square root of 10400, which is 102.</p>
60
<p>The second step is to multiply 102 with 5.</p>
60
<p>The second step is to multiply 102 with 5.</p>
61
<p>So 102 x 5 = 510.</p>
61
<p>So 102 x 5 = 510.</p>
62
<p>Well explained 👍</p>
62
<p>Well explained 👍</p>
63
<h3>Problem 4</h3>
63
<h3>Problem 4</h3>
64
<p>What will be the square root of (10000 + 400)?</p>
64
<p>What will be the square root of (10000 + 400)?</p>
65
<p>Okay, lets begin</p>
65
<p>Okay, lets begin</p>
66
<p>The square root is 102.</p>
66
<p>The square root is 102.</p>
67
<h3>Explanation</h3>
67
<h3>Explanation</h3>
68
<p>To find the square root, we need to find the sum of (10000 + 400). 10000 + 400 = 10400, and then √10400 = 102.</p>
68
<p>To find the square root, we need to find the sum of (10000 + 400). 10000 + 400 = 10400, and then √10400 = 102.</p>
69
<p>Therefore, the square root of (10000 + 400) is ±102.</p>
69
<p>Therefore, the square root of (10000 + 400) is ±102.</p>
70
<p>Well explained 👍</p>
70
<p>Well explained 👍</p>
71
<h3>Problem 5</h3>
71
<h3>Problem 5</h3>
72
<p>Find the perimeter of the rectangle if its length ‘l’ is √10400 units and the width ‘w’ is 50 units.</p>
72
<p>Find the perimeter of the rectangle if its length ‘l’ is √10400 units and the width ‘w’ is 50 units.</p>
73
<p>Okay, lets begin</p>
73
<p>Okay, lets begin</p>
74
<p>We find the perimeter of the rectangle as 304 units.</p>
74
<p>We find the perimeter of the rectangle as 304 units.</p>
75
<h3>Explanation</h3>
75
<h3>Explanation</h3>
76
<p>Perimeter of the rectangle = 2 × (length + width).</p>
76
<p>Perimeter of the rectangle = 2 × (length + width).</p>
77
<p>Perimeter = 2 × (√10400 + 50) = 2 × (102 + 50) = 2 × 152 = 304 units.</p>
77
<p>Perimeter = 2 × (√10400 + 50) = 2 × (102 + 50) = 2 × 152 = 304 units.</p>
78
<p>Well explained 👍</p>
78
<p>Well explained 👍</p>
79
<h2>FAQ on Square Root of 10400</h2>
79
<h2>FAQ on Square Root of 10400</h2>
80
<h3>1.What is √10400 in its simplest form?</h3>
80
<h3>1.What is √10400 in its simplest form?</h3>
81
<p>The prime factorization of 10400 is 2^4 x 5^2 x 13 x 20, so the simplest form of √10400 = √(2^4 x 5^2 x 13 x 20) = 102.</p>
81
<p>The prime factorization of 10400 is 2^4 x 5^2 x 13 x 20, so the simplest form of √10400 = √(2^4 x 5^2 x 13 x 20) = 102.</p>
82
<h3>2.Mention the factors of 10400.</h3>
82
<h3>2.Mention the factors of 10400.</h3>
83
<p>Factors of 10400 include 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 130, 160, 200, 208, 260, 325, 400, 416, 520, 650, 800, 1040, 1300, 2080, 2600, 5200, and 10400.</p>
83
<p>Factors of 10400 include 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 130, 160, 200, 208, 260, 325, 400, 416, 520, 650, 800, 1040, 1300, 2080, 2600, 5200, and 10400.</p>
84
<h3>3.Calculate the square of 10400.</h3>
84
<h3>3.Calculate the square of 10400.</h3>
85
<p>We get the square of 10400 by multiplying the number by itself, that is 10400 x 10400 = 108160000.</p>
85
<p>We get the square of 10400 by multiplying the number by itself, that is 10400 x 10400 = 108160000.</p>
86
<h3>4.Is 10400 a prime number?</h3>
86
<h3>4.Is 10400 a prime number?</h3>
87
<p>10400 is not a<a>prime number</a>, as it has more than two factors.</p>
87
<p>10400 is not a<a>prime number</a>, as it has more than two factors.</p>
88
<h3>5.10400 is divisible by?</h3>
88
<h3>5.10400 is divisible by?</h3>
89
<p>10400 has many factors, and it is divisible by numbers such as 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 130, 160, 200, 208, 260, 325, 400, 416, 520, 650, 800, 1040, 1300, 2080, 2600, 5200, and 10400.</p>
89
<p>10400 has many factors, and it is divisible by numbers such as 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 130, 160, 200, 208, 260, 325, 400, 416, 520, 650, 800, 1040, 1300, 2080, 2600, 5200, and 10400.</p>
90
<h2>Important Glossaries for the Square Root of 10400</h2>
90
<h2>Important Glossaries for the Square Root of 10400</h2>
91
<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 10^2 = 100, and the inverse of the square is the square root, which is √100 = 10. </li>
91
<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 10^2 = 100, and the inverse of the square is the square root, which is √100 = 10. </li>
92
<li><strong>Rational number:</strong>A rational number is a number that can be expressed in the form of p/q, where p and q are integers and q is not equal to zero. </li>
92
<li><strong>Rational number:</strong>A rational number is a number that can be expressed in the form of p/q, where p and q are integers and q is not equal to zero. </li>
93
<li><strong>Perfect square:</strong>A perfect square is a number that can be expressed as the square of an integer. For example, 100 is a perfect square as it can be expressed as 10^2. </li>
93
<li><strong>Perfect square:</strong>A perfect square is a number that can be expressed as the square of an integer. For example, 100 is a perfect square as it can be expressed as 10^2. </li>
94
<li><strong>Prime factorization:</strong>Prime factorization is the process of expressing a number as the product of its prime factors. </li>
94
<li><strong>Prime factorization:</strong>Prime factorization is the process of expressing a number as the product of its prime factors. </li>
95
<li><strong>Long division method:</strong>The long division method is a technique used to find the square root of a number by dividing the number into groups and finding the square root using division and subtraction.</li>
95
<li><strong>Long division method:</strong>The long division method is a technique used to find the square root of a number by dividing the number into groups and finding the square root using division and subtraction.</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>