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Concept of Square Roots

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  • Finding square roots

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Square Roots:

The inverse (opposite) operation of addition is subtraction and the inverse operation of multiplication is division. Similarly, finding the square root is the inverse operation of squaring.

We have,

122 =144, therefore square root of 144 is 12

92 = 81, therefore square root of 81 is 9.

Since 92 = 81, and (– 9)2 = 81

We say that square roots of 81 are 9 and – 9.

From the above, you may say that there are two integral square roots of a perfect square number.

The positive square root of a number is denoted by the symbol √.

For example: `sqrt(4) = 2 ("not"  – 2); sqrt(9) = 3 ("not" – 3)` etc.

Statement Inference Statement Inference
12 = 1 `sqrt(1) = 1` 62 = 36 `sqrt(36) = 6`
22 = 4 `sqrt(4) = 2` 72 = 49 `sqrt(49) = 7`
32 = 9 `sqrt(9) = 3` 82 = 64 `sqrt(64) = 8`
42 = 16 `sqrt(16) = 4` 92 = 81 `sqrt(81) = 9`
52 = 25 `sqrt(25) = 5` 102 = 100 `sqrt(100) = 10`
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