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# Simplify

0
47
2

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

May 22, 2022

#1
+280
0

(sqrt(29635200))/756 Then just simplify the square root

May 22, 2022
#2
+9457
0

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