simplify the square root below

Question

simplify the square root below √12x^22

Answer 1

√12x²² is the same as (12x²²)^1/2

 

By the product rule, you can separate this into 12^1/2  (x²²)^1/2 and then do each part separately.

 

When you take a power of a power, you multiply the two powers together, so (x²²)^1/2 = x¹¹

 

Again by the product rule, 12^1/2 = 4^1/2 * 3^1/2 = 2 * 3^1/2 = 2√3.

 

So 12^1/2  (x²²)^1/2 = 2√3 x¹¹ or 2x¹¹ √3