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Simplify $\frac{\sqrt{72}}{\sqrt{10} \cdot \sqrt{2} \cdot \sqrt{3} \cdot \sqrt{5}}$. Your answer should have an integer denominator.

 Jun 9, 2022

Best Answer 

 #1
avatar+1746 
+1

Simplify the denominator to: \(\sqrt{10 \times 2 \times 3 \times 5} = \sqrt{300} = 10 \sqrt 3\)

 

Now, simplify the numerator to: \(\sqrt{72} = 6 \sqrt 2\)

 

This means that the new fraction is: \({{ 6 \sqrt 2} \over {10 \sqrt 3 }} = {3 \sqrt 2 \over 5 \sqrt 3}\)

 

However, we need to rationalize the denominator by multiplying the fraction by \({5 \sqrt 3 } \over 5 \sqrt 3\). This will make the denominator an integer. 

 

Can you take it from here?

 Jun 9, 2022
 #1
avatar+1746 
+1
Best Answer

Simplify the denominator to: \(\sqrt{10 \times 2 \times 3 \times 5} = \sqrt{300} = 10 \sqrt 3\)

 

Now, simplify the numerator to: \(\sqrt{72} = 6 \sqrt 2\)

 

This means that the new fraction is: \({{ 6 \sqrt 2} \over {10 \sqrt 3 }} = {3 \sqrt 2 \over 5 \sqrt 3}\)

 

However, we need to rationalize the denominator by multiplying the fraction by \({5 \sqrt 3 } \over 5 \sqrt 3\). This will make the denominator an integer. 

 

Can you take it from here?

BuilderBoi Jun 9, 2022

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