Question

Simplify √(12/49)

Answer 1

(2/7) root 3.

Answer 2

\[\sqrt{\frac{12}{49}}=\frac{\sqrt{12}}{\sqrt{49}}\]

Answer 3

now you should be able to simplify \(\sqrt{49}\) first - do you know what the answer to this will be?

Answer 4

yes 7

Answer 5

correct, next we can write \(\sqrt{12}\) as:\[\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}\]

Answer 6

so here you should be able to simplify the \(\sqrt{4}\) term - what will that be?

Answer 7

why did you do that?

Answer 8

isnt your suppose to facotr the 12?

Answer 9

when you get a square root of something that itself is not a perfect square, then you should try and decompose it into the product of something which is a perfect square and something else

Answer 10

so isnt it 2x2x3?

Answer 11

the factors

Answer 12

so, since 12 is not a perfect square, we set it to be 4*3 because 4 is a perfect square

Answer 13

you could set 12=2*2*3, but that is unnecessary

Answer 14

oh ok so what do you do after that

Answer 15

the idea here is to find "perfect squares" in order to simplify the expression

Answer 16

so how would you find the answer?

Answer 17

what is the final answer in this case

Answer 18

ok, the last step was:\[\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}\]and I asked you what the value of \(\sqrt{4}\) would be?

Answer 19

2

Answer 20

correct, so now we put all the pieces together to get:\[\sqrt{49}=7\]\[\sqrt{12}=2\sqrt{3}\]therefore:\[\sqrt{\frac{12}{49}}=\frac{\sqrt{12}}{\sqrt{49}}=\frac{2\sqrt{3}}{7}\]

Answer 21

ohhh i see now thank you so so so much!

Answer 22

yw :)