Question

I am having a lot of problems in math right now. I am doing practice problems right now and I don't even understand them. I don't really understand it and I do online school. Any help would be appreciated.

1. What is the simplest form of the radical expression? Show all work.

3^3sqrt21 - 6^3sqrt2a

(The ^3's are attached to the sqrt, not the 3 and 6.)

2. Simplify. Show all work.

3^1/2 x 3^1/2

3. Rewrite ^nsqrtx^m using a rational expression. Show all work.

4. sqrt250x^16/sqrt2x Show all work

5. What is the solution of the equation? Show all work.

sqrt2x+13 - 5 = x

6. What is the solution of the equation? Show all work.

3 ^5sqrt(x+2)^3 + 3 = 27

(^5 is connected to sqrt.)

Answer 1

#1.
3^3sqrt21 - 6^3sqrt2a
Hard to say, but that appears to be
3∛21 - 6∛(2a)
Not much to do except factor out the 3
Unless you had a typo and meant
3∛21 - 6∛21 = -3∛21

#2. Using the properties of exponents,
3^1/2 x 3^1/2 = 3^(1/2 + 1/2) = 3^1 = 1

#3.
^nsqrtx = x^(1/n)
So, ^nsqrtx^m = (x^(1/n))^m = x^(m/n)

#4.
√(250x^16)/√(2x) = √(250x^16/2x) = √(125x^15) = √(25x^14 * 5x) = 5x^7 √(5x)

#5.
√(2x+13) - 5 = x
√(2x+13) = x+5
2x+13 = (x+5)^2 = x^2+10x+25
x^2+8x+12 = 0
(x+2)(x+6) = 0
x = -2, -6

#6.
^5sqrt(x+2)^3 + 3 = 27
^5sqrt(x+2)^3 = 24
(x+2)^3 = 24^5
x+2 = ∛(24^5)
x = ∛(24^5) - 2