Q34. - Algebra 1

Question

Estimate each square root to the nearest whole number.

$\sqrt{112}$

Step-by-Step Solution

Answer

The square root to the nearest whole number is 11.

Step 1. List some perfect squares.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169….

Step 2. Locate interval.

112 lies between 100 and 121.

Step 3. Find the nearest perfect square.

Distance of 112 from 100 = 112 – 100 = 12

Distance of 112 from 121 = 121 – 112 = 9

 

Since 9 < 12. So, 121 is closer to 112.

Step 4. Find the square root of the nearest perfect square

We know $121={11}^2$. So, $\sqrt{121}=11$.