## anonymous 5 years ago rationalize denominator 40 divided by sq. 5 * 40 divided by sq. 5

1. anonymous

Is this $$\frac{40}{\sqrt{5}}\cdot\frac{40}{\sqrt{5}}$$?

2. anonymous

yes

3. anonymous

40 / (sq. (5 * 40)) / sq.(5)? 40 * sq.(5) / (sq. (5 * 40) 40 / sq.(40) sq.(40) / 1

4. anonymous

Ah: 40 * 40 / 5 1600 / 5 320

5. anonymous

In that case, realize that when you multiply fractions, you multiply the numerators together and then the denominators together. Multiplying the denominators together you get $$\sqrt{5}^2$$, which is just 5. So the denominator rationalizes itself.

6. anonymous

That is not the way I did it but I came up with 5 over 5 which is 1

7. anonymous

Did you multiply the entire thing by $$\frac{\sqrt{5}}{\sqrt{5}}$$?

8. anonymous

no I simplified it came up with the common denominator I had 40 over 5 and then simplified it

9. anonymous

How did you simplify it?

10. anonymous

I see what I did wrong the answer is just 5

11. anonymous

If you keep it in fraction form and don't reduce, then yes. The final fraction is $$\frac{1600}{5}$$ as Supervisor put up there before he simplified to $$320$$.

12. anonymous

so you don't multiply 5*5

13. anonymous

So: \begin{align*} \frac{40}{\sqrt{5}}\cdot\frac{40}{\sqrt{5}} &= \frac{40\cdot 40}{\sqrt{5} \cdot \sqrt{5}}\\ &= \frac{40^2}{\sqrt{5}^2}\\ &= \frac{1600}{5} \end{align*}

14. anonymous

okay thank you