how do you do this?

Question

I was looking at the sheet that shows you what to expect on the test and I saw this problem and the answer and I cant figure how to solve it!!

the square root of 18 + the square root of 8 =

they said the answer was 5 and the square root of 2
could you explain how to get this please and thank you!

Answer 1

The thing to know is this:

sqrt(a * b) = sqrt(a) * sqrt(b)

This means that if you can factor a perfect square out of the number in the square root, you can take that factor out of the radical by taking its square root, leaving the quotient behind:

sqrt(18) + sqrt(8) =
sqrt(9*2) + sqrt(4*2) =
sqrt(9)*sqrt(2) + sqrt(4)*sqrt(2) =
3 * sqrt(2) + 2 * sqrt(2) =
(3 + 2) * sqrt(2) = // distributive property
5 * sqrt(2)

Answer 2

The sq root of 18 is the samet thing as the sq root of 9 X 2 which equals 3 X sq root of 2. By the same reasoning, the sq root of 8 equals sq root of 4 X 2 = 2 X sq root of 2. CCombining 3 X sq root of 2 + 2 X sq root of 2 yields 5 X sq root of 2. QED

Answer 3

A good try from your first respondent... remember the perfect squares,4,9, 16, 25 etc, and their roots
2,3,4,5
2x2=4
3x3=9 and so on. soooo in rad 18 you have 2x9 and in 8 you have 2x4 (both contain one of those perfect squares.... That's why you didn't pick 3x6 to get 18. Keep the perfect square numbers in mind as you solve radicals...

so under the rad sign you have rad 2x3^2 + 2x2^2

those numbers carrying a square, can come out of the rad sign. What is left, stays

3(rad2) + 2(rad2).

think of the rad 2 as, say x

3(x) + 2(x) = 5x
3(rad2) + 2(rad2) = 5(rad2)

Helpful?

Remember the arithmatic is supposed to be simple... they aren't going to ask you to multiply 7,896 by 4,563. They want to get a pattern across to you. If you read those last two aloud, you will see how well 'rad2' is just a big name for x.