Question

Compute the square root of 532 to the nearest tenth. Use the "divideand average method.

Answer 1

`\sqrt[]{532}\cong23.065`

Explanation:

We have the following square root

`\sqrt[]{532}`

We calculate by means of the divide and average method.

The first thing is to look for exact roots between those two values

Step 1 estimate

`\begin{gathered} \sqrt[]{539}<\sqrt[]{532}<\sqrt[]{576} \\ 23<\sqrt[]{532}<24 \\ \text{Estimate 23.5} \end{gathered}`

Step 2 divide

`(532)/(23.5)=22.63`

Step 3 average:

`(23.5+22.63)/(2)=(46.13)/(2)=23.065`

Therefore:

`\sqrt[]{532}\cong23.065`