Question concerning simplification of numerical expression with square roots.

[shamieh]

how does \(\displaystyle \frac{5700}{\sqrt{15,300}}\) turn into \(\displaystyle \frac{570}{\sqrt{153}}\) ??

 

[Ackbach]

how does \(\displaystyle \frac{5700}{\sqrt{15,300}}\) turn into \(\displaystyle \frac{570}{\sqrt{153}}\) ??

$$\frac{5700}{\sqrt{15,300}}=\frac{5700}{\sqrt{153 \cdot 100}}
=\frac{5700}{\sqrt{153} \sqrt{100}}=\frac{5700}{10\sqrt{153}}
=\frac{570}{\sqrt{153}}.$$