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Completely simplify and rationalize the denominator:$$\frac{\sqrt{160}}{\sqrt{252}}\times\frac{\sqrt{245}}{\sqrt{3}}$$

 May 22, 2022
 #1
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(sqrt(29635200))/756 Then just simplify the square root

 May 22, 2022
 #2
avatar+9461 
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The method hipie gave is also possible, but it is tedious. Instead, we could simplify the square roots on their own first.

 

\(\quad \dfrac{\sqrt{160}}{\sqrt{252}} \times \dfrac{\sqrt{245}}{\sqrt 3}\\ =\dfrac{4 \sqrt{10}}{6 \sqrt 7} \times \dfrac{7 \sqrt 5}{\sqrt 3}\\ = \dfrac{4\times 7}{6} \times \sqrt{\dfrac{10 \times 5}{7 \times 3}}\\ = \dfrac{4\times 7 \times \sqrt{10 \times 5 \times 7 \times 3}}{6\times 7 \times 3}\\ = \dfrac{2\sqrt{1050}}{9}\\ = \dfrac{10 \sqrt{42}}{9}\)

 May 22, 2022

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