Question

For questions 6-8, evaluate the

Answer 1

(6) The value of $\sqrt{64}$ is 8.

(7) The value of $-\sqrt{31}$ is -5.6

(8) The value of $-\sqrt{16}$ is -4

Explanation:

(6) The expression is $\sqrt{64}$

Since, 64 is a perfect square, this can be written as $8 \times 8$.

Thus, the expression can be written as

$\sqrt{64}=\sqrt{8 \times 8}=\sqrt{8^{2} }$

The square root gets cancelled. Thus, we have,

$\sqrt{64}=8$

Thus, the value of $\sqrt{64}$ is 8.

(7) The expression is $-\sqrt{31}$

Since, 31 is not a perfect square and solving the expression using a calculator, we get,

$-\sqrt{31}=-5.56776$

Rounding off to the nearest tenth, we get,

$-\sqrt{31}=-5.6$

Thus, the value of $-\sqrt{31}$ is -5.6

(8) The expression is $-\sqrt{16}$

Since, 16 is a perfect square, this can be written as $4\times 4$

Thus, the expression can be written as

$-\sqrt{16}=-\sqrt{4\times 4}=-\sqrt{4^{2} }$

The square root gets cancelled. Thus, we have,

$-\sqrt{16}=-4$

Thus, the value of $-\sqrt{16}$ is -4.