radical notation

Question

Write  the expression in radical notation;(6x)^1/4  

 

Answer 1

A ^1/2  = square root of A

 

A^1/3  = cube root of A

 

A^1/4 = fourth root of A,  etc

 

So, (6x)^1/4 = fourth root of 6x = ⁴√(6x)

Answer 2

Let's see if I can teach this quickly and efficiently.

 

x   x    x         x   x   x         x   x   x        x   x   x  = x¹²

 

 

    x3                   x3                x3                x3     =  (x³)⁴

 

 

 

    Note that (x³)⁴  =   x⁽³⁾⁽⁴⁾  or  x^{3 • 4}

 

 

Similarly  (x^0.5)^0.5  =  x^0.25

 

 

Since that, and since x^0.5 = √x

 

 

(x^0.5)^0.5 = √√x,  verbally spoken as square root of the square root of x;

 

 

Just one more thing.  You need to know that √(6x) = ( √6 ) ( √x );

 

So I think I got everything you need to figure out your answer.  Let someone know if you need more help.