Question

Estimate each square root to the nearest whole number.

$\sqrt{31}$

Short answer

The square root to the nearest whole number is 6.

Step-by-step solution

Step 1. List some perfect squares.

1, 4, 9, 16, 25, 36, 49,….

Step 2. Locate interval.

31 lies between 25 and 36.

Step 3. Find the nearest perfect square.

Distance of 31 from 25 = 31 – 25 = 6

Distance of 31 from 36 = 36 – 31 = 5

Since 5 < 6. So, 31 is closer to 36.

Step 4. Find square root of nearest perfect square.

We know $36=6^2$. So,$\sqrt{36}=6$