## Taxia2 Group Title how would you solve this rational equation? 2 months ago 2 months ago

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1. Taxia2 Group Title

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

2. myininaya Group Title

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

3. Taxia2 Group Title

oops, it is supposed to be simplified!

4. Taxia2 Group Title

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

5. myininaya Group Title

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 Group Title

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

7. Taxia2 Group Title

wouldn't that just be x?

8. myininaya Group Title

right another question! Do you know the distributive property?

9. Taxia2 Group Title

I do

10. myininaya Group Title

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

11. myininaya Group Title

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

12. myininaya Group Title

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

13. Taxia2 Group Title

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 Group Title

wait, I got it!!!

15. Taxia2 Group Title

I think...

16. myininaya Group Title

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 Group Title

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 Group Title

beautiful you didn't need my help

19. Taxia2 Group Title

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!