Question

Simplify:

√27x^2y^2

A) 27xy
B) 3xy
C) 3xy√3
D) xy√27

Answer 1

`√(27x^2y^2)=3xy\:√(3)`

Hence, option C is correct.

Explanation:

Given the expression

`√(27x^2y^2)`

simplifying the expression

`√(27x^2y^2)=√(27)√(x^2)√(y^2)`

Apply radical rule:
`√(a^2)=a,\:\quad \mathrm{\:assuming\:}a\ge 0`

`=√(27)x√(y^2)`

Apply radical rule:
`√(a^2)=a,\:\quad \mathrm{\:assuming\:}a\ge 0`

`=√(27)xy`

`=xy√(3^3)`

`=xy√(3^2\cdot \:\:3)`

Apply radical rule:
`√(a^2)=a,\:\quad \mathrm{\:assuming\:}a\ge 0`

`=3xy\:√(3)`

Therefore,

`√(27x^2y^2)=3xy\:√(3)`

Hence, option C is correct.