The process by which we can make opposite of square is called finding the square root. It is the opposite of squaring. It is a number that when multiplied by itself an indicated number of times forms a product equal to a specified number.
For example:
\(\sqrt{}\) represent the square root.
\(\sqrt{25}\) means the square root of 25
\(\sqrt{64}\) means square root of 64
A natural number are the perfect square root. Some of the natural numbers are 1, 4, 9, 16, etc.
For example: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 etc. are perfect squares.
A square root of a number can be done by two methods which make easy in the process of factorization. The two methods are:
Prime factorization method make easy in finding out the square root in the natural number.
It can be shown by the numerical examples:
1. Find the square root of 36.
Solution:
\(\sqrt{36}\)
= \(\sqrt{6 \times 6}\)
= 6
2. Find the square root of 2025.
Solution:
\(\sqrt{2025}\)
= \(\sqrt{9\times 9\times 5\times 5}\)
= 9×5
= 45
5 |
2025 |
5 |
405 |
9 |
81 |
9 |
Division method is a faster way to find out the square root of a number. It is less time consuming then the factorization method. For example, the number 512490 is grouped into three pairs of 51, 24, 90. If the number of digits in the number is odd then the first group will have one digit and rest will have two digits. For example, the number 18021 is grouped into three groups of 1, 80, 21. Cube Root.
In this method, we make the pair of digit whose square root has to be found. While pairing the digit we do it from the right side. So that if the number of digits is even then all group will have 2 digits and if a number of digits are odd then the first group has one and other will have two digits. For example, the number 512490 is grouped into three pairs of 51, 24, 90. If the number of digits in the number is odd then the first group will have one digit and rest will have two digits. For example, the number 18021 is grouped into three groups of 1, 80, 21. Cube Root.
Examples
1. Find the square root of 441
Solution:
\(\sqrt{441}\)
= \(\sqrt{3×3×7×7}\)
= 3× 7
= 21
2. Simplify: \(\sqrt{4^2×2^2}\)
Solution:
\(\sqrt{4^2×2^2}\)
= 4×2
= 8
.
Solution:
Square of 4
= 4^{2}
= 4×4
= 16
Solution:
Square of 10
= 10^{2}
= 10×10
= 100
Solution:
\(\sqrt{1+3}\)
= \(\sqrt{4}\)
= \(\sqrt{2×2}\)
= 2
Solution:
\(\sqrt{1+3+5}\)
= \(\sqrt{9}\)
=\(\sqrt{3×3}\)
= 3
Solution:
\(\sqrt{1+3+5+7.....+99}\)
= \(\frac{99+1}{2}\)
= \(\frac{100}{2}\)
= 50
Solution:
\(\sqrt{1+3+5+7}\)
= \(\sqrt{16}\)
=\(\sqrt{4×4}\)
= 4
Solution:
(0.2)^{2}
= (0.2)×(0.2)
= 0.04
Solution:
(0.01)^{2}
= (0.01)×(0.01)
=0.0001
Solution:
(-3)^{2}
= (-3)×(-3)
=9
Solution:
Square root of 81
=\(\sqrt{81}\)
=\(\sqrt{9×9}\)
=9
Solution:
square root of 256
= \(\sqrt{256}\)
= \(\sqrt{2 × 2 ×2 ×2 ×2× 2 ×2× 2}\)
= \(\sqrt{2^2× 2^2 ×2^2 ×2^2}\)
= 2 × 2 × 2 ×2
= 16
Solution:
square root of 676
=\(\sqrt{676}\)
= \(\sqrt{2×2×13×13}\)
= 2× 13
= 26
Solution:
\(\sqrt{2^2×3^2}\)
= 2 × 3
= 6
Solution:
\(\sqrt{12}\)
= \(\sqrt{2×2×3}\)
= 2\(\sqrt{3}\)
Solution:
= \(\sqrt{25x^6 ×4y^2}\)
= \(\sqrt{5×5×(x^3)^2×2×2×y^2}\)
= 5^{}× x^{3}× 2^{}× y
= 10x^{3}y
Find the squares of:
4
Find the squares of:
6
Find the squares of:
8
Find the squares of:
16
Find the squares of:
11
Find the squares of:
(frac{1}{2})
Find the squares of:
(frac{3}{4})
Find the squares of:
(frac{2}{3})
Find the squares of:
(frac{7}{10})
Find the square root of:
(frac{49}{64})
Find the square root of:
(frac{121}{256})
Find the square root of:
(frac{324}{625})
Find the square root of:
(frac{144}{400})
Find the square root by division method.
7225
Find the square root by division method.
2116
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Find the least number that should be subtracted to get a perfect square.4401610
Mar 05, 2017
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prabin
find the square root of 1026
Jan 23, 2017
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