Question

math help ss below

Answer 1

what's your first step?

Answer 2

\( 108 = 2^2 \times 3^3 \)
\( 252 = 2^2 \times 3^2 \times 7\)

\( 160 = 2^5 \times 5\)
\( 245 = 5 \times 7^2\)

Answer 3

oh ok
so 6sqrt(3), 6sqrt(7),4sqrt(10),5sqrt(7)

Answer 4

20sqrt(70)/36sqrt(21)?

Answer 5

Yeah you got it correct but make sure you're putting it in the right order


sqrt(160) / sqrt(252) * sqrt(245) / sqrt(108)


4 sqrt(10) / 6sqrt(7) * 7sqrt(5) / 6sqrt(3)

Answer 6

oh ok
24sqrt(70)/42sqrt(15)? how can i simplfy that

Answer 7

hmm no

Answer 8

\(\dfrac{4 \sqrt{10}}{ 6\sqrt{7}} \times \dfrac{ 7\sqrt{5}}{ 6\sqrt{3}}\)

Answer 9

and you should know

sqrt(10) * sqrt(5) = sqrt(5^2 *2)

Answer 10

simplify it as much as you can

Answer 11

and then we'll rationalize the denominator

Answer 12

ok so
sqrt(10*5)=sqrt(50)=5sqrt(2)
so (4*7*5)sqrt(2)/36sqrt(21)=140sqrt(2)/36sqrt(21)

Answer 13

Yes and now we have

\(\dfrac{140\sqrt{5}}{36\sqrt{21}}\)

To rationalize the denominator, you need to multiply by sqrt(21) to both the numerator and denominator

But if you first want to simplify it before doing that, then 140/36 can be simplified to 35/9

Answer 14

\(\dfrac{140\sqrt{5}}{36\sqrt{21}} = \dfrac{35\sqrt{5}}{9\sqrt{21}}\)

\( \dfrac{35\sqrt{5}}{9\sqrt{21}} \times \dfrac{\sqrt{21}}{\sqrt{21}} = ??\)

Answer 15

Rationalizing the denominator essentially means that there is no square root in the denominator and so we do that by multiply the numerator and denominator by that square root so that way we can eliminate it from the denominator

Answer 16

If you were to have something like \( 1 + \sqrt{5}\) in the denominator

we would have to multiply it by the CONJUGATE of that which is \( 1 - \sqrt{5}\)

the conjugate of a + b is is a -b
the conjugate of a - b is a + b

this is just a little bit more advanced in case you encounter a question like that but if/when you do, you can always post it and we can go over it then

but essentially the concept of the conjugate is that we're using the formula
(a+b)(a-b) = a^2 - b^2
and it helps us get rid of the square root in the denominator

Answer 17

ok so its 35sqrt(105)/189?

Answer 18

yeah, and we can simplify 35 and 189

35 = 5 * 7
189 = 7 * 27

so what is

\(\dfrac{35\sqrt{105}}{189} = ?\)

Answer 19

ok so
5sqrt(105)/27

Answer 20

And you're all done now!

Answer 21

it says im wrong?

Answer 22

hmm

we made a mistake somewhere along the way

https://www.wolframalpha.com/input/?i=sqrt%28160%29+%2F+sqrt%28252%29+*+sqrt%28245%29%2Fsqrt%28108%29

Answer 23

\(\dfrac{140\sqrt{2}}{36\sqrt{21}} = \dfrac{35\sqrt{2}}{9\sqrt{21}}\)

\( \dfrac{35\sqrt{2}}{9\sqrt{21}} \times \dfrac{\sqrt{21}}{\sqrt{21}} = ??\)

and that will get us the correct answer

Answer 24

ok so
35sqrt(42)/189=5sqrt(42)/27

Answer 25

Yup! That should be the answer

Apologies for my oversight

Answer 26

its ok thanks for helping

Answer 27

My pleasure :)