## anonymous 4 years ago The square root of 8x times the square root of 8x

1. nikita2

$\sqrt{8x}\sqrt{8x}$ ?

2. nikita2

= 8x and x>=0

3. anonymous

Can you explain better how you got that?

4. TuringTest

$\sqrt a\times\sqrt a=(\sqrt a)^2=a$

5. anonymous

Actually the original problem is the square root of 5 divided by the square root of 8x. Can you show the whole process because I'm really confused

6. anonymous

But i understand how the square roots cancel out

7. nikita2

$\sqrt{5}/\sqrt{8x} = \sqrt{\left(\begin{matrix}5 \\ 8x\end{matrix}\right)}$

8. anonymous

I need to rationalize the denominator

9. TuringTest

$\frac{\sqrt5}{\sqrt{8x}}=\frac{\sqrt5}{\sqrt{2^3x}}\cdot\frac{\sqrt{2x}}{\sqrt{2x}}=\frac{\sqrt{10x}}{4x}$

10. anonymous

Why don't i multiply the numerator and denominator by the swuare root of 8x?? why do i have to break it up

11. TuringTest

$\frac{\sqrt5}{\sqrt{8x}}=\frac{\sqrt5}{\sqrt{8x}}\cdot\frac{\sqrt{8x}}{\sqrt{8x}}=\frac{\sqrt{40x}}{\sqrt{64x^2}}=\frac{2\sqrt{10x}}{8x}=\frac{\sqrt{10x}}{4x}$

12. anonymous

wait i thought you said $\sqrt{8x } * \sqrt{8x} = 8x$

13. TuringTest

yeah it does, look at the denominator. it winds up as 8x, then simplifies to 4x

14. anonymous

and on the last step you just divided the top and bottum by 2 to get rid of it?

15. TuringTest

yeah

16. anonymous

ok thank you!

17. TuringTest

no prob