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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    Is this \(\frac{40}{\sqrt{5}}\cdot\frac{40}{\sqrt{5}}\)?

  2. anonymous
    • 5 years ago
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    yes

  3. anonymous
    • 5 years ago
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    40 / (sq. (5 * 40)) / sq.(5)? 40 * sq.(5) / (sq. (5 * 40) 40 / sq.(40) sq.(40) / 1

  4. anonymous
    • 5 years ago
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    Ah: 40 * 40 / 5 1600 / 5 320

  5. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    That is not the way I did it but I came up with 5 over 5 which is 1

  7. anonymous
    • 5 years ago
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    Did you multiply the entire thing by \(\frac{\sqrt{5}}{\sqrt{5}}\)?

  8. anonymous
    • 5 years ago
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    no I simplified it came up with the common denominator I had 40 over 5 and then simplified it

  9. anonymous
    • 5 years ago
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    How did you simplify it?

  10. anonymous
    • 5 years ago
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    I see what I did wrong the answer is just 5

  11. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    so you don't multiply 5*5

  13. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    okay thank you

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