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kiamonstaa

  • 2 years ago

what is the exact value of the expression?

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  1. kiamonstaa
    • 2 years ago
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    \[\sqrt{45}-\sqrt{75}+\sqrt{192}\]

  2. helder_edwin
    • 2 years ago
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    \[ \large \sqrt{45}=\sqrt{5\cdot9}=3\sqrt{5} \]

  3. helder_edwin
    • 2 years ago
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    do the same with the other roots.

  4. kiamonstaa
    • 2 years ago
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    for the sqrt75 i got sqrt5*7*2

  5. kiamonstaa
    • 2 years ago
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    im stuck there

  6. satellite73
    • 2 years ago
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    i think \(75=25\times 3\)

  7. helder_edwin
    • 2 years ago
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    right

  8. kiamonstaa
    • 2 years ago
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    ohh..makes sense

  9. satellite73
    • 2 years ago
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    making \(\sqrt{75}=\sqrt{25\times 3}=\sqrt{25}\times \sqrt{3}=5\sqrt{3}\)

  10. helder_edwin
    • 2 years ago
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    now do the same with 192

  11. helder_edwin
    • 2 years ago
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    \[ \large \sqrt{192}= \]

  12. kiamonstaa
    • 2 years ago
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    would it be 4sqrt6?

  13. helder_edwin
    • 2 years ago
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    i got \[ \large \sqrt{192}=\sqrt{2^6\cdot3}=2^3\cdot\sqrt{3}=8\sqrt{3} \]

  14. kiamonstaa
    • 2 years ago
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    oh okay. i missed a 2

  15. kiamonstaa
    • 2 years ago
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    so how would i simplify all that?

  16. helder_edwin
    • 2 years ago
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    now plug in everything: \[ \large \sqrt{45}-\sqrt{75}+\sqrt{192}=3\sqrt{5}-5\sqrt{3}+8\sqrt{3} \]

  17. helder_edwin
    • 2 years ago
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    now combine like terms.

  18. kiamonstaa
    • 2 years ago
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    do you add or multiply?

  19. helder_edwin
    • 2 years ago
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    add or substract

  20. kiamonstaa
    • 2 years ago
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    oh okay so 6 sqrt 11?

  21. goformit100
    • 2 years ago
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    yeah

  22. kiamonstaa
    • 2 years ago
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    okay thx

  23. helder_edwin
    • 2 years ago
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    \[ \large =3\sqrt{5}+3\sqrt{3}=3(\sqrt{5}+\sqrt{3}) \]

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