Hello Reiny, please check these problems for me and if they are not right WOULD YOU PLEASE HELP ME WITH THE CORRECT ONES THANKS!!!

1. Slove for X, wher X is the real number, square root 5x + 9= square root 9x + 13= 27
2. Find the value: ^3 square root -27= 9
3. Write the following in simplified radical form ^4 square root 80= 4
PLEASE HELP QUICKLY!!

1 . I assume you meant

√(5x+9) = √(9x+13)
if so, then square both sides
5x + 9 = 9x + 13
-4x = 4
x = -1, the answer checks in my equation

2. I can't figure out what you are saying.
are you finding the cuberoot of -27 ?
if so, the cuberoot of -27 = -3

3 again, is that supposed to the fourth root of 80 ?

80^(1/4) = (16)^(1/4) (5)^(1/4)
= 2 times cuberoot of 5

last line should have said

2 times fourthroot of 5

THANKS AGAIN Reiny!!

Sure, I can help you with these problems. Let's go through each one step by step.

1. Solve for X: √(5x + 9) = √(9x + 13) = 27

To solve this equation, we need to isolate the variable x.

First, let's square both sides of the equation to eliminate the square root.

(√(5x + 9))^2 = (√(9x + 13))^2 = 27^2

Simplifying the left side gives us:

5x + 9 = (9x + 13)

Now, let's simplify the right side:

27^2 = 729

Next, move all the terms with x to one side of the equation by subtracting 9x from both sides:

-4x + 9 = 13

Now, subtract 9 from both sides:

-4x = 4

To solve for x, divide both sides of the equation by -4:

x = -1

So the solution to the equation is x = -1.

2. Find the value: ∛(-27) = 9

To find the value, we need to find a number that, when cubed, will equal -27.

In this case, the number is -3, as (-3)^3 = -27.

So the value of ∛(-27) is -3.

3. Write the following in simplified radical form: ⁴√80 = 4

To write the expression in simplified radical form, we need to express 80 as a product of powers of prime numbers.

80 can be broken down into 16 * 5, and further, 16 can be expressed as 4^2.

So, 80 = 4^2 * 5.

Rewriting the original expression using this information:

⁴√(4^2 * 5)

Since the index is 4 and the exponent is 2, we can rewrite the expression as:

4 * ⁴√5

Therefore, the simplified radical form of ⁴√80 is 4 * ⁴√5.

I hope this helps! Let me know if you have any other questions.