can someone please correct this for me thanks.

simplify:

7sqrt(7x) + 5 sqrt (7x)

My work:

(7+5)sqrt (7x)

My answer:

12sqrt (7x)

is this correct?

yup

so i don't have to take out the x from the radicand

Nope.

7x + 5x = 12x

No matter what "x" is.

To simplify the expression 7sqrt(7x) + 5sqrt(7x), you did it correctly by combining the coefficients outside the square root. The sum of 7 and 5 is indeed 12, so the simplified expression is 12sqrt(7x). Therefore, your answer is correct.

Regarding your second question about taking out the x from the radicand, in this case, you don't need to separate out the x because both terms inside the square root have the same radicand, which is 7x. Since the terms have identical radicands, they can be combined directly without any further simplification.