What is the simplest radical form of 7200 and then 288?

Answer 1

Radicals, or square roots

sqrt(7200)

We can split sqrt(7200) into 2 pieces, perfect square numbers, and... well, the ones that aren't.

sqrt(7200) = sqrt(3600*2)

sqrt(7200) = sqrt(36)*sqrt(100)*sqrt(2)

3600 is a perfect square, 2 is not. However, I'll continue breaking it down to make it easier to calculate.

sqrt(7200) = 6*10*sqrt(2) = 60*sqrt(2)

Since the square root of 36 is 6, and square root of 100 is 10.

You can break square roots up like this using multiplication.

However, I can't do anything to sqrt(2) because there is no (real) number times itself to give me 2.

Your final answer would be 60 radical 2 (or 60 sqrt(2))

---- sqrt(288)

Similarly, let's break 288 into factors that are perfect squares, and not perfects.

sqrt(288) = sqrt(144*2)

sqrt(288) = sqrt(144)*sqrt(2)

sqrt(288) = 12 * sqrt(2)

final answer: 12 sqrt(2) or 12 rad 2