1.) 6√24x, for which value of x makes the expression equivalent to 18√24?

a.) 3
b.) 9
c.) 12
d.) 18

My answer: C.

2.) 4√72x, for which value of x makes the expression equivalent to 24√72?

a.) 6
b.) 7
c.) 36
d.) 72

My answer: A.

3.) 7√32x, for which value of x makes the expression equivalent to 28√32?

a.) 4
b.) 8
c.) 14
d.) 16

My answer: B.

I will do the first one:

6√24x = 18√24
divide by √24
6x = 18
x = 3

do the others the same way,

#1 and #3 are incorrect, you had #2 correct

btw, I interpreted you question as you typed it.
I assume you did not mean
6√(24x)

1.) To find the value of x that makes the expression 6√24x equivalent to 18√24, we can set up the equation:

6√24x = 18√24

First, let's simplify the square root terms. √24 can be written as 2√6.

6 * 2√6 * x = 18 * 2√6

12√6x = 36√6

To simplify further, we can divide both sides of the equation by √6.

12x = 36

Dividing both sides by 12, we get:

x = 3

Therefore, the correct answer is a.) 3.

2.) Similar to the previous problem, let's set up the equation:

4√72x = 24√72

Simplifying the square root terms, we have:

4 * 2√18 * x = 24 * 2√18

8√18x = 48√18

Dividing both sides by √18, we get:

8x = 48

Dividing both sides by 8, we find:

x = 6

Therefore, the correct answer is a.) 6.

3.) Let's set up the equation:

7√32x = 28√32

Simplifying the square root terms, we have:

7 * 2√8 * x = 28 * 2√8

14√8x = 56√8

Dividing both sides by √8, we get:

14x = 56

Dividing both sides by 14, we find:

x = 4

Therefore, the correct answer is a.) 4.

To solve these questions, we need to set the given expression equal to the expression we want it to be equivalent to and solve for x.

1.) 6√24x = 18√24

To begin, we can simplify the expressions by dividing both sides by √24.

6x = 18

Next, divide both sides by 6 to isolate the variable x.

x = 3

Therefore, the value of x that makes the expression equivalent to 18√24 is 3. Checking the options given, the correct answer is a.) 3.

2.) 4√72x = 24√72

Similar to the previous question, let's simplify the expressions by dividing both sides by √72.

4x = 24

Next, divide both sides by 4 to solve for x.

x = 6

Therefore, the value of x that makes the expression equivalent to 24√72 is 6. Checking the options given, the correct answer is a.) 6.

3.) 7√32x = 28√32

Again, let's simplify by dividing both sides by √32.

7x = 28

Divide both sides by 7 to solve for x.

x = 4

Hence, the value of x that makes the expression equivalent to 28√32 is 4. Checking the options given, the correct answer is a.) 4.