2 added
2 removed
Original
2026-01-01
Modified
2026-02-28
1
-
<p>347 Learners</p>
1
+
<p>394 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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1680.</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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1680.</p>
4
<h2>What is the Square Root of 1680?</h2>
4
<h2>What is the Square Root of 1680?</h2>
5
<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 1680 is not a<a>perfect square</a>. The square root of 1680 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1680, whereas (1680)^(1/2) is in the exponential form. √1680 ≈ 40.9878, 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.<strong></strong></p>
5
<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 1680 is not a<a>perfect square</a>. The square root of 1680 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1680, whereas (1680)^(1/2) is in the exponential form. √1680 ≈ 40.9878, 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.<strong></strong></p>
6
<h2>Finding the Square Root of 1680</h2>
6
<h2>Finding the Square Root of 1680</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>and approximation methods 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>and approximation methods 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 1680 by Prime Factorization Method</h2>
11
</ul><h2>Square Root of 1680 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 1680 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 1680 is broken down into its prime factors.</p>
13
<p><strong>Step 1:</strong>Finding the prime factors of 1680 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 5 x 7 = 2^4 x 3^1 x 5^1 x 7^1</p>
13
<p><strong>Step 1:</strong>Finding the prime factors of 1680 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 5 x 7 = 2^4 x 3^1 x 5^1 x 7^1</p>
14
<p><strong>Step 2:</strong>Now we have found the prime factors of 1680. The second step is to make pairs of those prime factors. Since 1680 is not a perfect square, the digits of the number can’t be grouped in complete pairs.</p>
14
<p><strong>Step 2:</strong>Now we have found the prime factors of 1680. The second step is to make pairs of those prime factors. Since 1680 is not a perfect square, the digits of the number can’t be grouped in complete pairs.</p>
15
<p>Therefore, calculating √1680 using prime factorization is not straightforward, but it can be approximated.</p>
15
<p>Therefore, calculating √1680 using prime factorization is not straightforward, but it can be approximated.</p>
16
<h3>Explore Our Programs</h3>
16
<h3>Explore Our Programs</h3>
17
-
<p>No Courses Available</p>
18
<h2>Square Root of 1680 by Long Division Method</h2>
17
<h2>Square Root of 1680 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<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. 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 1680, we need to group it as 80 and 16.</p>
19
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1680, we need to group it as 80 and 16.</p>
21
<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 16. We can say n is '4' because 4 x 4 = 16. Now the<a>quotient</a>is 4, and after subtracting 16 - 16, the<a>remainder</a>is 0.</p>
20
<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 16. We can say n is '4' because 4 x 4 = 16. Now the<a>quotient</a>is 4, and after subtracting 16 - 16, the<a>remainder</a>is 0.</p>
22
<p><strong>Step 3:</strong>Bring down 80, which is the new<a>dividend</a>. Double the old<a>divisor</a>to get 8, which will be our new divisor.</p>
21
<p><strong>Step 3:</strong>Bring down 80, which is the new<a>dividend</a>. Double the old<a>divisor</a>to get 8, which will be our new divisor.</p>
23
<p><strong>Step 4:</strong>The new divisor will be 8n, and we need to find the value of n.</p>
22
<p><strong>Step 4:</strong>The new divisor will be 8n, and we need to find the value of n.</p>
24
<p><strong>Step 5:</strong>The next step is finding 8n x n ≤ 80. Let us consider n as 9, now 8 x 9 = 72.</p>
23
<p><strong>Step 5:</strong>The next step is finding 8n x n ≤ 80. Let us consider n as 9, now 8 x 9 = 72.</p>
25
<p><strong>Step 6:</strong>Subtract 80 from 72; the difference is 8, and the quotient is 49.</p>
24
<p><strong>Step 6:</strong>Subtract 80 from 72; the difference is 8, and the quotient is 49.</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 800.</p>
25
<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 800.</p>
27
<p><strong>Step 8:</strong>Find the new divisor, which is 89 because 891 x 1 = 891.</p>
26
<p><strong>Step 8:</strong>Find the new divisor, which is 89 because 891 x 1 = 891.</p>
28
<p><strong>Step 9:</strong>Subtracting 891 from 800, we get the result -91.</p>
27
<p><strong>Step 9:</strong>Subtracting 891 from 800, we get the result -91.</p>
29
<p><strong>Step 10:</strong>Now the quotient is 40.9.</p>
28
<p><strong>Step 10:</strong>Now the quotient is 40.9.</p>
30
<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point, or continue until the remainder is zero.</p>
29
<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point, or continue until the remainder is zero.</p>
31
<p>So the square root of √1680 is approximately 40.99.</p>
30
<p>So the square root of √1680 is approximately 40.99.</p>
32
<h2>Square Root of 1680 by Approximation Method</h2>
31
<h2>Square Root of 1680 by Approximation Method</h2>
33
<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 1680 using the approximation method.</p>
32
<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 1680 using the approximation method.</p>
34
<p><strong>Step 1:</strong>Now we have to find the closest perfect squares around √1680. The smallest perfect square less than 1680 is 1600, and the largest perfect square more than 1680 is 1764. √1680 falls somewhere between 40 and 42.</p>
33
<p><strong>Step 1:</strong>Now we have to find the closest perfect squares around √1680. The smallest perfect square less than 1680 is 1600, and the largest perfect square more than 1680 is 1764. √1680 falls somewhere between 40 and 42.</p>
35
<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>:</p>
34
<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>:</p>
36
<p>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>
35
<p>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>
37
<p>Using the formula: (1680 - 1600) / (1764 - 1600) = 80 / 164 ≈ 0.48.</p>
36
<p>Using the formula: (1680 - 1600) / (1764 - 1600) = 80 / 164 ≈ 0.48.</p>
38
<p>Using the formula, we identified the<a>decimal</a>point of our square root.</p>
37
<p>Using the formula, we identified the<a>decimal</a>point of our square root.</p>
39
<p>The next step is adding the value we got initially to the decimal number, which is 40 + 0.48 ≈ 40.98, so the square root of 1680 is approximately 40.98.</p>
38
<p>The next step is adding the value we got initially to the decimal number, which is 40 + 0.48 ≈ 40.98, so the square root of 1680 is approximately 40.98.</p>
40
<h2>Common Mistakes and How to Avoid Them in the Square Root of 1680</h2>
39
<h2>Common Mistakes and How to Avoid Them in the Square Root of 1680</h2>
41
<p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Let us look at a few of those mistakes students tend to make in detail.</p>
40
<p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Let us look at a few of those mistakes students tend to make in detail.</p>
41
+
<h2>Download Worksheets</h2>
42
<h3>Problem 1</h3>
42
<h3>Problem 1</h3>
43
<p>Can you help Max find the area of a square box if its side length is given as √1680?</p>
43
<p>Can you help Max find the area of a square box if its side length is given as √1680?</p>
44
<p>Okay, lets begin</p>
44
<p>Okay, lets begin</p>
45
<p>The area of the square is approximately 1680 square units.</p>
45
<p>The area of the square is approximately 1680 square units.</p>
46
<h3>Explanation</h3>
46
<h3>Explanation</h3>
47
<p>The area of the square = side^2. The side length is given as √1680. Area of the square = (√1680)^2 = 1680. Therefore, the area of the square box is approximately 1680 square units.</p>
47
<p>The area of the square = side^2. The side length is given as √1680. Area of the square = (√1680)^2 = 1680. Therefore, the area of the square box is approximately 1680 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 1680 square feet is built; if each of the sides is √1680, what will be the square feet of half of the building?</p>
50
<p>A square-shaped building measuring 1680 square feet is built; if each of the sides is √1680, 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>840 square feet</p>
52
<p>840 square feet</p>
53
<h3>Explanation</h3>
53
<h3>Explanation</h3>
54
<p>We can divide the given area by 2 as the building is square-shaped. Dividing 1680 by 2 = 840. So half of the building measures 840 square feet.</p>
54
<p>We can divide the given area by 2 as the building is square-shaped. Dividing 1680 by 2 = 840. So half of the building measures 840 square feet.</p>
55
<p>Well explained 👍</p>
55
<p>Well explained 👍</p>
56
<h3>Problem 3</h3>
56
<h3>Problem 3</h3>
57
<p>Calculate √1680 x 5.</p>
57
<p>Calculate √1680 x 5.</p>
58
<p>Okay, lets begin</p>
58
<p>Okay, lets begin</p>
59
<p>Approximately 204.94</p>
59
<p>Approximately 204.94</p>
60
<h3>Explanation</h3>
60
<h3>Explanation</h3>
61
<p>The first step is to find the square root of 1680, which is approximately 40.99. The second step is to multiply 40.99 by 5. So, 40.99 x 5 ≈ 204.94</p>
61
<p>The first step is to find the square root of 1680, which is approximately 40.99. The second step is to multiply 40.99 by 5. So, 40.99 x 5 ≈ 204.94</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 (1600 + 80)?</p>
64
<p>What will be the square root of (1600 + 80)?</p>
65
<p>Okay, lets begin</p>
65
<p>Okay, lets begin</p>
66
<p>The square root is 42.</p>
66
<p>The square root is 42.</p>
67
<h3>Explanation</h3>
67
<h3>Explanation</h3>
68
<p>To find the square root, we need to find the sum of (1600 + 80). 1600 + 80 = 1680, and then √1680 ≈ 42. Therefore, the square root of (1600 + 80) is approximately 42.</p>
68
<p>To find the square root, we need to find the sum of (1600 + 80). 1600 + 80 = 1680, and then √1680 ≈ 42. Therefore, the square root of (1600 + 80) is approximately 42.</p>
69
<p>Well explained 👍</p>
69
<p>Well explained 👍</p>
70
<h3>Problem 5</h3>
70
<h3>Problem 5</h3>
71
<p>Find the perimeter of the rectangle if its length ‘l’ is √1680 units and the width ‘w’ is 50 units.</p>
71
<p>Find the perimeter of the rectangle if its length ‘l’ is √1680 units and the width ‘w’ is 50 units.</p>
72
<p>Okay, lets begin</p>
72
<p>Okay, lets begin</p>
73
<p>We find the perimeter of the rectangle as approximately 181.98 units.</p>
73
<p>We find the perimeter of the rectangle as approximately 181.98 units.</p>
74
<h3>Explanation</h3>
74
<h3>Explanation</h3>
75
<p>Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√1680 + 50) ≈ 2 × (40.99 + 50) = 2 × 90.99 ≈ 181.98 units.</p>
75
<p>Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√1680 + 50) ≈ 2 × (40.99 + 50) = 2 × 90.99 ≈ 181.98 units.</p>
76
<p>Well explained 👍</p>
76
<p>Well explained 👍</p>
77
<h2>FAQ on Square Root of 1680</h2>
77
<h2>FAQ on Square Root of 1680</h2>
78
<h3>1.What is √1680 in its simplest form?</h3>
78
<h3>1.What is √1680 in its simplest form?</h3>
79
<p>The prime factorization of 1680 is 2 x 2 x 2 x 2 x 3 x 5 x 7, so the simplest form of √1680 = √(2^4 x 3 x 5 x 7).</p>
79
<p>The prime factorization of 1680 is 2 x 2 x 2 x 2 x 3 x 5 x 7, so the simplest form of √1680 = √(2^4 x 3 x 5 x 7).</p>
80
<h3>2.Mention the factors of 1680.</h3>
80
<h3>2.Mention the factors of 1680.</h3>
81
<p>Factors of 1680 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, and 1680.</p>
81
<p>Factors of 1680 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, and 1680.</p>
82
<h3>3.Calculate the square of 1680.</h3>
82
<h3>3.Calculate the square of 1680.</h3>
83
<p>We get the square of 1680 by multiplying the number by itself, which is 1680 x 1680 = 2,822,400.</p>
83
<p>We get the square of 1680 by multiplying the number by itself, which is 1680 x 1680 = 2,822,400.</p>
84
<h3>4.Is 1680 a prime number?</h3>
84
<h3>4.Is 1680 a prime number?</h3>
85
<p>1680 is not a<a>prime number</a>, as it has more than two factors.</p>
85
<p>1680 is not a<a>prime number</a>, as it has more than two factors.</p>
86
<h3>5.1680 is divisible by?</h3>
86
<h3>5.1680 is divisible by?</h3>
87
<p>1680 has many factors; it is divisible by 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, and 1680.</p>
87
<p>1680 has many factors; it is divisible by 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, and 1680.</p>
88
<h2>Important Glossaries for the Square Root of 1680</h2>
88
<h2>Important Glossaries for the Square Root of 1680</h2>
89
<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, which is √16 = 4. </li>
89
<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, which is √16 = 4. </li>
90
<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>
90
<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>
91
<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. This is why it is also known as the principal square root. </li>
91
<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. This is why it is also known as the principal square root. </li>
92
<li><strong>Perfect square:</strong>A perfect square is a number that can be expressed as the square of an integer. For example, 16 is a perfect square because it equals 4^2. </li>
92
<li><strong>Perfect square:</strong>A perfect square is a number that can be expressed as the square of an integer. For example, 16 is a perfect square because it equals 4^2. </li>
93
<li><strong>Long division method:</strong>This is a method used to find the square root of a non-perfect square number by dividing it into smaller, manageable parts.</li>
93
<li><strong>Long division method:</strong>This is a method used to find the square root of a non-perfect square number by dividing it into smaller, manageable parts.</li>
94
</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
94
</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
95
<p>▶</p>
95
<p>▶</p>
96
<h2>Jaskaran Singh Saluja</h2>
96
<h2>Jaskaran Singh Saluja</h2>
97
<h3>About the Author</h3>
97
<h3>About the Author</h3>
98
<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>
98
<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>
99
<h3>Fun Fact</h3>
99
<h3>Fun Fact</h3>
100
<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
100
<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>