How do you simplify (sqrt9sqrt8)/(sqrt6sqrt6)?

2 Answers
Mar 30, 2017

sqrt2

Explanation:

(sqrt9sqrt8)/(sqrt6sqrt6)=(3*sqrt(2*4))/6

=(3*2sqrt(2))/6=(6sqrt2)/6

=sqrt2

Mar 30, 2017

There are different methods which can be used:

First option: Combine the radicals:

(sqrt9sqrt8)/(sqrt6sqrt6) = sqrt72/sqrt36 = sqrt(72/36) = sqrt2

Second option: Simplify where possible, find factors of radicands.

(color(red)(sqrt9)color(blue)(sqrt8))/(color(green)(sqrt6sqrt6))

=(color(red)(3)color(blue)(sqrt(4xx2)))/(color(green)(sqrt6)^2)

=(color(red)(3)color(blue)(xx2sqrt(2)))/(color(green)(6)

=sqrt2

Third option: Write as the product of prime factors:

(sqrt9sqrt8)/(sqrt6sqrt6)

=(sqrt3 xx sqrt3 xxsqrt2xx sqrt2xx sqrt2)/(sqrt2xxsqrt3xxsqrt2xx sqrt3)" " now cancel

=(cancelsqrt3 xx cancelsqrt3 xxcancelsqrt2xx cancelsqrt2xx sqrt2)/(cancelsqrt2xxcancelsqrt3xxcancelsqrt2xx cancelsqrt3)

=sqrt2