Question

Estimate the value of the following numbers to the nearest whole number
(i) $\sqrt{97}$
(ii) $\sqrt{250}$
(iii) $\sqrt{780}$

Answer 1

(i) $\sqrt{97}$

We know that, $81<97<100$

$\Rightarrow 9^2<97<{10}^2$

$\Rightarrow 9<\sqrt{97}<10$

Therefore, $\sqrt{97}$ to the nearest whole number is $10$.

(ii) $\sqrt{250}$

We know that, $225<250<256$

$\Rightarrow {15}^2<250<{16}^2$

$\Rightarrow 15<\sqrt{250}<16$

Therefore, $\sqrt{250}$ to the nearest whole number is $16$

(iii) $\sqrt{780}$

We know that, $729<780<784$

$\Rightarrow {27}^2<780<{28}^2$

$\Rightarrow 27<\sqrt{780}<28$

Therefore, $\sqrt{780}$ to the nearest whole number is $28$