SOLUTION: This is 5 different problems I've been having problems with for a while. 4/sqrt5 4sqrtx^12/24sqrtx^12 15sqrt8x^16/5sqrt2x^4 (3sqrt5)(2sqrt10) (2sqrtx)(5sqrtx^3)

Question 200938: This is 5 different problems I've been having problems with for a while.
4/sqrt5
4sqrtx^12/24sqrtx^12
15sqrt8x^16/5sqrt2x^4
(3sqrt5)(2sqrt10)
(2sqrtx)(5sqrtx^3)
Found 2 solutions by jim_thompson5910, jsmallt9:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first three to get you going in the right direction.

# 1

Start with the given expression.

Multiply both the numerator and denominator by

Combine the roots.

Multiply

Take the square root of 25 to get 5

So

# 2

Start with the given expression.

Factor 24 to get 4*6

Cancel out the common terms.

Simplify

Combine the roots

Divide

Simplify

So where

# 3

Start with the given expression.

Factor 15 into 5*3

Cancel out the common terms.

Simplify

Combine the roots.

Factor 8 into 4*2

Cancel out the common terms.

Simplify

Divide the variable terms by subtracting the exponents.

Subtract

Factor into note: there are 6 terms.

Break up the square root using the identity .

Take the square root of to get .

Take the square root of to get .

Multiply.

==================================================

Answer:

So simplifies to

In other words, where

Edit: The other poster is correct in saying that "x" doesn't need to be non-negative, BUT recall that . If we assume that (ie it is NOT negative), then which simplifies things greatly. If "x" can be any number, then you must include the absolute value.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
I just want to correct something in the solutions of jimthompson5910:

In problems #2 and #3, x does not have to be positive. x could be positive or negative. The only number x cannot be is zero.
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