what is the simplest form of the radical expression?

Question

√75-4√18+2√32
show all steps

Answer 1

To simplify the given radical expression, we can first simplify each radical term under the square root.

√75 = √(25 * 3) = √25 * √3 = 5√3

√18 = √(9 * 2) = √9 * √2 = 3√2

√32 = √(16 * 2) = √16 * √2 = 4√2

Now substitute these simplified terms back into the original expression:

5√3 - 4(3√2) + 2(4√2)
= 5√3 - 12√2 + 8√2
= 5√3 - 4√2

Therefore, the simplest form of the expression √75 - 4√18 + 2√32 is 5√3 - 4√2.