Question

(b) Without using a calculator, the square root of 18 will be between what two values (remember to look for perfect squares/perfect square roots)? Show your reasoning. You do not need to find the decimal equivalent of the root.

Answer 1

√18 = 3√2

Explanation:

the square root of 18 = √18

18;

1 × 18 = 18

2 × 9 = 18

3 × 6 = 18

6 × 3 = 18

9 × 2 = 18

18 × 1 = 18

9 has a perfect square

So,

√18 = √(2*9)

= √2 * √9

= 3√2

√18 = 3√2

Perfect square

1 × 1 = 1

2 × 2 = 4

3 × 3 = 9

4 × 4 = 16

5 × 5 = 25

Therefore,

√18 is between 4 and 5