Question

Simplify √((4x^2)/(3y))

Answer 1

`(2)/(3)(x√(3y))/(y)`

Explanation:

`\sqrt{(4x^2)/(3y) }`, by laws of roots,
`\sqrt{(a)/(b)}=(√(a))/(√(b))`, so
`(√(4x^2))/(√(3y))`, and by laws of roots,
`√(ab)=√(a)√(b)`, therefore
`\frac{√(4){√(x^2)}}{√(3)√(y)}`, since only the numerator simplifies into real numbers, keep the
`√(3y)`, or,
`(√(4)√(x^2))/(√(3y))`, then
`√(4)=2` and
`√(x^2)=x`, therefore,
`(√(4)√(x^2))/(√(3y))=(2x)/(√(3y))`. Then in order to rationalize the denominator, multiply both the numerator and denominator by the denominator, or,
`√(3y)`, therefore,
`(2x)/(√(3y))((√(3y))/(√(3y)))=(2x√(3y))/(3y)=(2)/(3)(x√(3y))/(y)`