Question

What is the simplified fraction form of 15xsqrt(3)/sqrt(75x^2)?

Answer 1

\[\large \frac{15x\sqrt{3}}{\sqrt{75x^2}}\] first simplify the denominator \[\large \sqrt{75 x^2} = \sqrt{ \color{blue}{25}\cdot 3 \color{magenta}{\cdot x \cdot x}}\]

Answer 2

\[\large \sqrt{75 x^2} = \sqrt{ \color{blue}{25}\cdot 3 \color{magenta}{\cdot x \cdot x}}= \sqrt{\color{blue}{5 \cdot 5} \cdot 3 \cdot \color{magenta}{x \cdot x}}\] anything you can pull out of the square root?

Answer 3

5

Answer 4

and what else? :)

Answer 5

the x's

Answer 6

good job. that leaves you with \[\large \color{blue}5\color{magenta}x\sqrt{3}\] correct?

Answer 7

Yes

Answer 8

Now that we've factored out our denominator,lets rewrite the problem :D \[\large \frac{15x\sqrt{3}}{5x\sqrt{3}}\] is there any like-terms we can cancel out here?

Answer 9

the sqrt(3)

Answer 10

Yes that's one. Anything else?

Answer 11

The x's

Answer 12

Thats two! anything we can simplify? :)

Answer 13

Ya the 15 and 5 go to 3

Answer 14

\[\large \frac{15\cancel x\ \cancel{\sqrt{3}}}{5\cancel x\ \cancel{\sqrt{3}}}\]

Answer 15

good! and you got your answer :)

Answer 16

So the answer is 3

Answer 17

Yep.

Answer 18

And to check this we can plug 3 back into our original equation \[\large \frac{15x\sqrt{3}}{\sqrt{75x^2}}\] x = 3 \[\large \frac{15(3)\sqrt{3}}{\sqrt{75(3)^2}} = 3\]

Answer 19

\[\large \frac{45\sqrt{3}}{\sqrt{675}}= 3\] the reduced form. plug this into your calculator :)