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# Algebra

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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

#1
+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
+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?

BuilderBoi Jun 9, 2022