Question

rationalize denominator
40 divided by sq. 5 * 40 divided by sq. 5

Answer 1

Is this \(\frac{40}{\sqrt{5}}\cdot\frac{40}{\sqrt{5}}\)?

Answer 2

yes

Answer 3

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

Answer 4

Ah:
40 * 40 / 5
1600 / 5
320

Answer 5

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.

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

How did you simplify it?

Answer 10

I see what I did wrong the answer is just 5

Answer 11

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 \(320\).

Answer 12

so you don't multiply 5*5

Answer 13

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

Answer 14

okay thank you