Question

Help??? Assuming x >0, what is the simplified fraction form for 15x times sqrt(3) all divided by sqrt(75x^2)?

Answer 1

\[\frac{ 15x \sqrt{3} }{ \sqrt{ 75 x^2} }\]

Answer 2

I think that its 3/1 is that it?

Answer 3

I would do it step by step.
do you know how to simplify sort(x^2) ?

Answer 4

*sqrt(x^2)

Answer 5

\[ \sqrt{x^2} = x \]
or
\[ \sqrt{x \cdot x} = x \]
if you have a pair multiplied together inside a square root sign, you can replace it with a single copy with no root sign.

so
\[ \sqrt{2\cdot 2} = 2 \]
or
\[ \sqrt{a\cdot a} = a \]

Answer 6

\( x^2 \) is short-hand for \(x\cdot x\)
so what is \(\sqrt{x^2} \)?

Answer 7

\[\sqrt{x^2}\] is equal to x

Answer 8

yes, so the fraction is now
\[ \frac{15x\sqrt{3}}{x\sqrt{75} } \]
x divided by x is one, so you can "cancel" them
\[ \frac{15\cancel{x}\sqrt{3}}{\cancel{x}\sqrt{75} } = \frac{15\sqrt{3}}{\sqrt{75} } \]

Answer 9

now to simplify the \(\sqrt{75}\) break up the 75 into its prime factors
75= 3*5*5
\[ 75= \sqrt{3⋅5⋅5}\]
do you see any pairs that you can "pull out" of the square root?

Answer 10

Just noticed 5*5*5=125 we want 3*5*5= 75

Answer 11

Sorry I was gone, I to have dinner. Okay so can you take out the pair of 5s ?

Answer 12

yes, the bottom becomes \(5 \sqrt{3} \)

Answer 13

\[\frac{15\sqrt{3}}{5\sqrt{3}} \]

Answer 14

do the square roots of 3 cancel out on the numerator and denominator?

Answer 15

yes anything divided by itself (except 0/0) is 1

it is a very useful thing to know.

Answer 16

okay and then 15/5 is equal to 3/1 or just 3 right?

Answer 17

Awesome! Thank you so much for helping me do this problem, The steps are clearer now and it will make similar problems easier for me!