# What is a radical of 136?

##### 1 Answer

See explanation...

#### Explanation:

The first kind of radical you meet is a square root, written:

#sqrt(136)#

This is the positive irrational number (

That is:

#sqrt(136) * sqrt(136) = 136#

The prime factorisation of

#136 = 2^3*17#

Since this contains a square factor, we find:

#136 = sqrt(2^2*34) = sqrt(2^2)*sqrt(34) = 2sqrt(34)#

Note that

#(-sqrt(136))^2 = (sqrt(136))^2 = 136#

Beyond square roots, the next is the cube root - the number which when cubed gives the radicand.

#root(3)(136) = root(3)(2^3*17) = root(3)(2^3)root(3)(17) = 2root(3)(17) ~~ 5.142563#

For any positive integer

#root(n)(136)#

with the property that:

#(root(n)(136))^n = 136#