Question concerning simplification of numerical expression with square roots.

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SUMMARY

The numerical expression $$\frac{5700}{\sqrt{15,300}}$$ simplifies to $$\frac{570}{\sqrt{153}}$$ through the application of square root properties and simplification techniques. The process involves recognizing that $$15,300$$ can be factored into $$153 \cdot 100$$, allowing the square root to be separated into $$\sqrt{153}$$ and $$\sqrt{100}$$. This results in the final simplification of the expression by dividing the numerator by 10, yielding $$\frac{570}{\sqrt{153}}$$.

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shamieh
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how does $$\frac{5700}{\sqrt{15,300}}$$ turn into $$\frac{570}{\sqrt{153}}$$ ??
 
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shamieh said:
how does $$\frac{5700}{\sqrt{15,300}}$$ turn into $$\frac{570}{\sqrt{153}}$$ ??

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

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