Simple Algebra Questions - Radicals?

Question

Hi i need help with these simple algebra questions , these are the only ones i am stuck on. It is for Algebra II. We are currently on the topic of simplifying radical expressions.


1. sqrt(40 a^3 b^4)

2. 2 * sqrt (24m^4n^5)^ (1/3)
( which reads as 2 multipled by the third root of 24m^4n^5)

3. sqrt( (1/32)w^6 z^7) ^ (1/5)
( which reads as the fifth root of 1/32 w^6z^7

step by step?

Answer 1

1)sqrt(2^3x5xa^3b^4)=2ab^2sqrt(10a)
2)2sqrt(2^3x3xm^4n^5)^1/3=4mnsqrt(3mn^2)^1/3
3)1/2wz^2sqrt(wz^2)^1/5

Answer 2

Are you at the point where you've been told to assume √x² = x and not fuss that it should really be |x| ? If so, then

1. √(40a³b^4) = 2ab²√(10a)
2. 2[cube root](24m^4n^5) = 2[2mn][cube root](3mn²) = 4mn[cube root](3mn²)
3. [5th root][(1/32)(w^6)(z^7)] = (1/2)wz[5th root][wz²]