# Introduction of Square Roots

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**Introduction of square roots :**The square root of a number a is that number which when multiplied by itself gives a as the product.

Thus, if b is the square root of a number a, then

b x b = a or b

^{2}= a.

The square root symbol is √a

It follows from this that

b = √a ⇔ b

^{2}= a.

i. e. b is the square root of a if and only if a is the square of b.

Example: 1) Square root of 16 is 4

(√16 = 4)

2) Square root of 3 is not a whole number.

(√3=1.73)

3)Square root of 9 is 3

(√9 = 3)

**Example on finding the square roots**:

(i) √ 4 = 2, because 2

^{2}= 4.

(ii) √9 = 3, because 3

^{2}= 9.

(iii) √324 = 18, because 18

^{2}= 324.

(iv) √1225 = 35, because 35

^{2}= 1225.

(v) √10,000 = 100, because 100

^{2}= 10,000.

(vi) √a

^{2}= a, because a

^{2}= a x a.

**Remark:**Since 4 = 2

^{2}= (-2)

^{2}, therefore 2 and -2 can both be the square roots of 4.

However we agree that the square of a number will be taken to positive square root only . Thus, √4 = 2.

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**Practice**

1)√13x13 = -----

2) √c x c = -----

3) √19 x19 = -----

4) √(d x d x a x a) = -----

5) √10 x10 = -----

**Squares and Square roots**

• Introduction of Squares and Square Roots

• Perfect Squares or not

• Properties of Square Numbers

• Short cut method to find squares

• Introduction of Square Roots

• Properties of Square Roots

• Square root by Prime factorization method

• Square root by long division method

• Square root of rational numbers

• Square root of Decimals

• Square root by estimation method

• Introduction of Squares and Square Roots

• Perfect Squares or not

• Properties of Square Numbers

• Short cut method to find squares

• Introduction of Square Roots

• Properties of Square Roots

• Square root by Prime factorization method

• Square root by long division method

• Square root of rational numbers

• Square root of Decimals

• Square root by estimation method

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