ANSWER:
[tex]\sqrt[]{532}\cong23.065[/tex]STEP-BY-STEP EXPLANATION:
We have the following square root
[tex]\sqrt[]{532}[/tex]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
[tex]\begin{gathered} \sqrt[]{539}<\sqrt[]{532}<\sqrt[]{576} \\ 23<\sqrt[]{532}<24 \\ \text{Estimate 23.5} \end{gathered}[/tex]Step 2 divide
[tex]\frac{532}{23.5}=22.63[/tex]Step 3 average:
[tex]\frac{23.5+22.63}{2}=\frac{46.13}{2}=23.065[/tex]Therefore:
[tex]\sqrt[]{532}\cong23.065[/tex]