Question

express the sum in simplest form

Answer 1

\[4\sqrt{7} +8\sqrt{63}\]

Answer 2

Well, we can't add together radicals unless they have the same radicand (the number under the root).
We have to check if there are any perfect squares in the radicand since we can pull those out.
7 is prime, so there's nothing to do there.
Are there any perfect square factors for 63? (4*? = 63, 9*?=63... ?)

Answer 3

8*7

Answer 4

8*7 = 56... 9*7 does seem to work, though
\[ \sqrt{63} = \sqrt{9*7} = \sqrt{9}\sqrt{7} = 3\sqrt{7} \]

Answer 5

then, we can just replace sqrt(63) with 3sqrt(7) in the expression and simplify. We'll have the same radicand then, and so we can add them together
4sqrt(7) + 8(3sqrt(7))

Answer 6

12

Answer 7

what do we do with the 3 square

Answer 8

\[ 4\sqrt{7} + 8*(3\sqrt{7}) \]
We have to multiply the 8*3 first. Also, when we add, the radical won't disappear. We'll just add the numbers in front and the square root will follow

Answer 9

24

Answer 10

Yes. We can then add that to the 4 root 7

Answer 11

basically, when we add radicals, we're actually factoring the radical out and adding the numbers multiplied to the radicals... like this:
\[ 4\sqrt{7} + 24\sqrt{7} = \sqrt{7}*(4 + 24) = \sqrt{7}*(28) \]

Answer 12

kk

Answer 13

what happens to