Simplify the square root

Question

3√(-27y^7x^5z^6)

 

Answer 1

So lets break this apart using the properties of the square root. 

 

3√(-27y⁷x⁵z⁶) = 3(√-27)(√y⁷)(√x⁵)(√z⁶)

 

√-27 = √(9)(-3) = 3√-3

√y⁷ = √(y⁶)(y) = (y³)(√y)

√x⁵ = √(x⁴)(x) = (x²)(√x)

√z⁶ = z³

 

Simplifying it all we get 3(3√-3)(y³)(√y)(x²)(√x)(z³) = 9y³x²z³√(-3xy)

 

Hope this helps!