simplify the radicals...

Question

√2*^5√5

 

 

and 

 

^16√x^36

Answer 1

√(2)* ⁵√(5)

There's really not much that can be simplified here. The bases and degrees are both different. If you want to write this with exponents instead of roots, it would be

2^1/2 * 5^1/5

 

¹⁶√(x³⁶)

Here, you can simplify by writing as an exponent, and removing the whole parts of the exponent as a factor outside of the radical.

x^(36/16) = x^(9/4)= x²*x^(1/4) = x² * ⁴√(x)

 

Alternately, you could remove 16*2 from the original root, then reduce it.

¹⁶√(x³²*x⁴) = x² * ¹⁶√(x⁴) = x² * ⁴√(x)