# Quantitative Reasoning Square Root Question

#### ephesus32

10+ Year Member
7+ Year Member
Hi,

The fourth root of x^3 times the square root of x equals 32. what is x?

Can somebody systematically take me to this? Thanks. I'm getting to point where it is X^(5/4)=32, but don't know how to get the answer easily after that. Thanks.

#### sciencegod

##### Super Member
10+ Year Member
problem is messed up. try it. plug 16 in for x its not 32.

#### ephesus32

10+ Year Member
7+ Year Member
problem is messed up. try it. plug 16 in for x its not 32.
hmmmm.. I don't think it's messed up. Plugging in 16 works for me in the calculator. Try it again, I'm sure you'll get it.

#### Sublimation

10+ Year Member
5+ Year Member
Hi,

The fourth root of x^3 times the square root of x equals 32. what is x?

Can somebody systematically take me to this? Thanks. I'm getting to point where it is X^(5/4)=32, but don't know how to get the answer easily after that. Thanks.

This is actually simple if you think SAT math. Look they drew it out like that so you get confused. remember that the square root of something is that thing ^.5. Just do the same thing here express the problem in a way that you can work it out as such

4Roots of (x^3) is the same as saying X^(3/4)
so multiply tat by X^(1/2) and you get

X^(3/4) . X^(1/2) = X^[(3/4)+(1/2)] =32
Then solve X^(5/4)=32

32^4/5 is 16 =X

#### ephesus32

10+ Year Member
7+ Year Member
This is actually simple if you think SAT math. Look they drew it out like that so you get confused. remember that the square root of something is that thing ^.5. Just do the same thing here express the problem in a way that you can work it out as such

4Roots of (x^3) is the same as saying X^(3/4)
so multiply tat by X^(1/2) and you get

X^(3/4) . X^(1/2) = X^[(3/4)+(1/2)] =32
Then solve X^(5/4)=32

32^4/5 is 16 =X

Thanks Sublimation.
However, 32^(4/5) is kind of time consuming for the QC section doing it mathematically especially getting the fifth square root. Is there any better time efficient way to figure it out?

#### Streetwolf

##### Ultra Senior Member
10+ Year Member
7+ Year Member
Yeah. Know that the fifth root of 32 is 2. That should be something you remember.

And even if you didn't know... it's the 5th root! Anything to the 5th power makes it a LOT bigger. And since 32 isn't exactly that large of a number, it makes sense that you should think that 2 is the 5th root.

Last edited:

#### sciencegod

##### Super Member
10+ Year Member
streetwolf is mathgod.

#### joonkimdds

##### Senior Member
10+ Year Member
7+ Year Member
streetwolf is mathgod.
can I be PATgod since science and math god are already assigned? #### ephesus32

10+ Year Member
7+ Year Member
thanks streetwolf... that explains a lot