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sasho [114]
3 years ago
8

10. Simplify the rational expression by rationalizing the denominator. 3 sqrt 160/sqrt 1350x A) 2 sqrt 15x/15x B) 3 sqrt 160/135

0x C) 4 sqrt 15x/15x D) 4/ sqrt 45x 11.
Mathematics
1 answer:
Viefleur [7K]3 years ago
7 0
The simplified expression by rationalizing the denominator is (C)\frac{4 \sqrt{15x} }{15x}.

First we must simplify the expression:
\frac{3 \sqrt{160} }{\sqrt{1350x} } =  \frac{12 \sqrt{10} }{15 \sqrt{6x} } =  \frac{4 \sqrt{10} }{5 \sqrt{6x} }

Then we factor the rational parts and cancel it out:
\frac{4 \sqrt{2} \sqrt{5} }{5 \sqrt{2} \sqrt{3x} } = \frac{4\sqrt{5} }{5\sqrt{3x} }

Then we rationalize the expression:
\frac{4\sqrt{5} }{5\sqrt{3x} } * \frac{\sqrt{3x} }{\sqrt{3x} } = \frac{4 \sqrt{15x} }{5*3x} = \frac{4 \sqrt{15x} }{15x}

<span>Finally, the simplified expression by rationalizing the denominator is (C)\frac{4 \sqrt{15x} }{15x}.</span>
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