simplify the following radical expression: 4 sqrt(625)

a) sqrt (25)
b) 25
c)5
d) no solution exists

c

If the problem is asking for the fourth root of 625, then c is correct. That would be the case if the 4 is in the crook of the radical sign.

To simplify the given radical expression, 4sqrt(625), we start by finding the square root of 625.

The square root of 625 is 25, since 25 multiplied by itself (25 * 25) equals 625.

Now, we can simplify the expression as follows:

4sqrt(625) = 4 * 25 = 100.

Thus, the simplified form of the given radical expression is 100.

Out of the options provided:

a) sqrt (25) is equal to 5, which is not the same as 100.
b) 25 is not equal to 100.
c) 5 is not equal to 100.
d) No solution exists does not apply in this case.

Therefore, the correct answer is d) no solution exists.