what is the simplest form of the radical expression?
√75-4√18+2√32
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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.