Question

Simplify 162x3y2−−−−−−−√ . Assume x and y are nonnegative.

Answer 1

`9xy√(2x)`

Explanation:

Given expression is,

`√(162x^3y^2)`

`=(162x^3y^2)^(1)/(2)`
`(\because \sqrt[n]{x} =x^(1)/(n))`

`=162^(1)/(2)(x^3)^(1)/(2) (y^2)^(1)/(2)`
`(\because (ab)^m=a^mb^m)`

`=(81* 2)^(1)/(2) x^{3* (1)/(2)} y^{2* (1)/(2)}`

`=(81)^(1)/(2) (2)^(1)/(2) x^{(3)/(2)} y^{(2)/(2)}`

`=9(2)^(1)/(2) x^{1+(1)/(2)} y^1`

`=9(2)^(1)/(2) x^(1).x^{(1)/(2)} y`
`(\because a^(m+n)=a^m.a^n )`

`=9xy(2x)^(1)/(2)`

`=9xy√(2x)`