1

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Square Roots

Squares and Square Roots

Finding Square Roots

Squares and Square Roots

2

What is square root?

Squares and Square Roots

3

The square root of a number is defined as follows.

If x2 = a,

then x is a square root of a.

The radical sign ‘ ’ is used to denote the square roots

of a number.

The positive and negative square roots of any positive

number a can be represented by and

respectively.

a a

172 = (– 17)2 = 289

The square roots of 289 are 17 and –17.

Squares and Square Roots

4

Example 1

Write down the square roots of 289 without using a calculate.

Squares and Square Roots

5

Example 2

Evaluate . without using a calculator. 222 2510

= 222 2510 425100

= 11

= 121

6

How can we find the

positive square root of

any positive number?

Finding Square Roots

7

Finding Square Roots

To find the positive square root of any positive

number, we can use the key ‘ ’ in the calculator.

e.g. (a) = 12

Result: 3.464101615

Keying sequence: EXE 12

(b) = 25013

Result: 158.1549873

Keying sequence: EXE 25013

(c) = 22 73

Result: 7.615773106

Keying sequence: EXE 58 58

3.5 , cor. to 1 d.p.

158.15 , cor. to 2 d.p.

= 7.616 , cor. to 3 d.p.