Question

Simplify:4sqrt400/4sqrt5

Answer 1

\[\sqrt{400} = \sqrt{4}\sqrt{100}\]

Answer 2

have a go at the rest

Answer 3

8.9 or 9

Answer 4

@poopereat, no this doesn't seem to be the correct answer. Using alekos first answer, you should first simplify \[\sqrt{4}\] then simplify \[\sqrt{100}\]before multiplying them together. Both of these are perfect squares so you shouldn't have decimals.

Answer 5

sqrt 4 = 1.4
sqrt 100= 10
14/ 2.24= 6.25?

Answer 6

Ok, so sqrt(4) does not equal 1.4.
What number, when multiplied by itself, is equal to 4?

Answer 7

2

Answer 8

Correct, so that means the sqrt(4) = 2.
You were correct that sqrt(100) = 10.
So what happens when you take (sqrt(4)) * (sqrt(100))?

Answer 9

20

Answer 10

Great! There's your answer. The key is to split the 400 into two numbers that you know it is divisible by (4 and 100) and find the square roots of those two numbers. Later you'll encounter problems where both numbers may not be perfect roots so you'll have something like sqrt(147) = sqrt(49) * sqrt(3) = \[7\sqrt{3}\] where the sqrt(3) doesn't simplify any further and you would leave it at that. Just fyi.

Answer 11

20/ 8.96 = 2.23

Answer 12

I'm sorry I totally missed the 4s in the original equation. The 4 on top will cancel with the 4 on bottom like so:
Since the sqrt(5) isn't simplified any further you want to leave it as sqrt(5) to be called an exact answer.