## Taxia2 11 months ago how would you solve this rational equation?

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1. Taxia2

$\sqrt{15x}(\sqrt{18x}+\sqrt{15x})$

2. myininaya

There is no equation to solve? Are you to multiply?

3. Taxia2

oops, it is supposed to be simplified!

4. Taxia2

but that is the equation, I have the answer, but I am unsure how to get to it.

5. myininaya

So we want to simplify the expression. Again there is no equation. Just so you know assuming we have x>=0 you can write $\sqrt{18x}=\sqrt{18} \sqrt{x}$ and you can also do the same for the other terms too.

6. myininaya

Do you know how to multiply $\sqrt{x} \cdot \sqrt{x}?$

7. Taxia2

wouldn't that just be x?

8. myininaya

right another question! Do you know the distributive property?

9. Taxia2

I do

10. myininaya

so you know if you have a(b+c) you can do ab+ac

11. myininaya

so you have $\sqrt{15} \sqrt{x}(\sqrt{18} \sqrt{x}+\sqrt{15} \sqrt{x})$

12. myininaya

so you can treat the thing on the outside of the parenthesis just like that a above

13. Taxia2

yes, but wouldn't all of the square roots cancel out? I tried this but the answer i received had no square roots in it. But the answer that is given does...

14. Taxia2

wait, I got it!!!

15. Taxia2

I think...

16. myininaya

Is 15*18 a perfect square? I don't think it is. So you would have at least one square root in your answer. What do you think the answer is?

17. Taxia2

well, the given answer is $3x \sqrt{30} +15x$ so first I simplified what i could inside the parenthesis and got $\sqrt{15x} (3\sqrt{2x} + \sqrt{15x})$ and then I distributed (Like you said!) and got this $3\sqrt{30x ^{2}} + \sqrt{15^{2}x ^{2}}$ then I canceled out the roots (like you said) and got the answer!

18. myininaya

beautiful you didn't need my help

19. Taxia2

I did! If I hadn't had it I probably would have given up (as cliche as that sounds) Thank you so much for working me through it!