Question

Please help
Find the difference of 9√7 and √28

Answer 1

Ok, in order to subtract (or add) radicals, we need the same value underneath the square roots. So, lets look at the square root of 28. Remember, if 28 has a factor that is a perfect square, we can square root it and put it in front.

Do you know which factor of 28 is a perfect square?

Answer 2

Um honestly no I'm not to sure

Answer 3

is it 7?

Answer 4

Ok, we could try listing all the factors of 28:
1, 2, 4, 7, 14, 28
Which of those numbers is a perfect square? (Other than 1)

Answer 5

7

Answer 6

7 isn't a perfect square, because we can't take a whole number, square it, and get 7. Lets list some perfect squares:
2 squared is 4 <---
3 squared is 9
4 squared is 16

4 is a perfect square because it is equal to 2 times 2

Answer 7

okay so ?

Answer 8

So, since the square root of 4 is 2, we can pull out the two to the front. Whats left in the radical is 28/4=7. So:
\[\sqrt{28}=\sqrt{4} \times \sqrt{7}=2\sqrt{7}\]So what does this mean for the original problem? Well:
\[9\sqrt{7} - \sqrt{28}=9\sqrt{7} - 2\sqrt{7} = ?\]

Answer 9

7√7?

Answer 10

yes

Answer 11

yay !

Answer 12

like roots add each other

Answer 13

thank u