Algebra

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Completely simplify and rationalize the denominator: $\frac{\sqrt{160}}{\sqrt{252}}\times\frac{\sqrt{245}}{\sqrt{180}}$

Guest Jul 23, 2021

CPhill · Answer 1 · 2021-07-23T05:36:59

sqrt (160) = sqrt (16 *10) = 4sqrt 10

sqrt (252) = sqrt (36 * 7) = 6sqrt 7

sqrt (245) = sqrt ( 49 * 5) = 7sqrt 5

sqrt (180) = sqrt (36 * 5) = 6 sqrt (5)

So we have

4sqrt (10) 7 sqrt (5) 28sqrt (10)

_________ * __________ = ____________ =

6 sqrt (7) 6 sqrt (5) 36 sqrt (7)

(7/9) sqrt ( 10) / sqrt (7) =

(7/9) sqrt (70) / 7 =

sqrt ( 70) * 7/63 =

sqrt (70) / 9