Q35. - Algebra 1

Question

Estimate each square root to the nearest whole number.

$\sqrt{152}$

Step-by-Step Solution

Answer

The square root to the nearest whole number is 12.

Step 1. List some perfect squares.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196….

Step 2. Locate interval.

152 lies between 144 and 169.

Step 3. Find the nearest perfect square.

Distance of 152 from 144 = 152 – 144 = 8

Distance of 152 from 169 = 169 – 152 = 17

 

Since 8 < 17. So, 144 is closer to 152.

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

We know $144={12}^2$. So, $\sqrt{144}=12$.