MHB Question concerning simplification of numerical expression with square roots.

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The expression $$\frac{5700}{\sqrt{15,300}}$$ simplifies to $$\frac{570}{\sqrt{153}}$$ by recognizing that 15,300 can be factored into 153 and 100. The square root of the product is then separated into the product of the square roots, leading to $$\frac{5700}{\sqrt{153} \cdot \sqrt{100}}$$. Simplifying further, the square root of 100 equals 10, allowing the expression to be rewritten as $$\frac{5700}{10\sqrt{153}}$$. Dividing 5700 by 10 results in 570, confirming the simplification.
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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 $$\frac{570}{\sqrt{153}}$$ ??

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

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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