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anonymous

  • 4 years ago

HOW DO I FIGURE THIS OUT \[6\sqrt{2} - 3\sqrt{2}\]

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  1. KingGeorge
    • 4 years ago
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    \[6\sqrt{2} - 3\sqrt2 = \sqrt{2} \cdot (6-3) =3\sqrt2\]

  2. anonymous
    • 4 years ago
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    how do i do these? \[\sqrt{90} , \sqrt{125}, 4\sqrt{20}\]

  3. KingGeorge
    • 4 years ago
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    What do you want to do with them? Just simplify them as much as possible?

  4. anonymous
    • 4 years ago
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    no have an anser like \[9\sqrt{10} or 10\sqrt{9} examples\]

  5. anonymous
    • 4 years ago
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    This one i dont get either \[5\sqrt{10} * 3\sqrt{?}\]

  6. anonymous
    • 4 years ago
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    i ment to put * \[3\sqrt{8}\]

  7. KingGeorge
    • 4 years ago
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    Let's start with the first one.\[\sqrt{90} = \sqrt{9} \cdot \sqrt{10} = 3\sqrt{10}\]similarly, \[\sqrt{125} = \sqrt{25} \cdot \sqrt{5} = 5\sqrt5\]and\[4\sqrt{20} = 4\sqrt{4} \cdot \sqrt5 = 4 \cdot 2 \cdot \sqrt5 = 8\sqrt5\]

  8. anonymous
    • 4 years ago
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    \[7\sqrt{72}\]

  9. KingGeorge
    • 4 years ago
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    As for that last problem, \[5\sqrt{10} \cdot 3\sqrt8 = 15 \cdot \sqrt{10} \cdot \sqrt8 = 15 \cdot \sqrt{80}=15 \cdot \sqrt{16} \cdot \sqrt5 = 60\sqrt5\]Is it clear what you have to do for these problems now?

  10. anonymous
    • 4 years ago
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    i dont get the one i posted or the 4/20 one.

  11. anonymous
    • 4 years ago
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    would this one \[\sqrt{8} * \sqrt{3}\] = \[\sqrt{24}\]?

  12. anonymous
    • 4 years ago
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    would this one \[\sqrt{8} * \sqrt{3}\] = \[\sqrt{24}\]?

  13. KingGeorge
    • 4 years ago
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    That would be correct. Good job! As for the other problems, give me a few more seconds to finish typing up the response...

  14. anonymous
    • 4 years ago
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    KK :)

  15. KingGeorge
    • 4 years ago
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    Well, both the 7/72 and 4/20 are basically the same problem with different numbers. You have an expression with some number outside the radical (4 and 7), and a number inside (20 and 72). At the beginning, you can just ignore the number outside. Then simplify the radical as much as possible. In this case, \[\sqrt{72} = \sqrt{36} \cdot \sqrt2 = 6\sqrt2\]and \[\sqrt{20} = \sqrt4 \cdot \sqrt5 =2\sqrt5\]Then, to finish it all off, you multiply by the number you originally had in front. So,\[7\sqrt{72}=7\cdot(6\sqrt2) = 42\sqrt2\]\[4\sqrt{20}=4\cdot (2\sqrt5)=8\sqrt5\]And those would be the final answers. Also, with the square root of 24, it would be better to then simplify like so\[\sqrt{24} = \sqrt4 \cdot \sqrt6 = 2\sqrt6\]

  16. anonymous
    • 4 years ago
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    i see... ok. Thanks so much!

  17. KingGeorge
    • 4 years ago
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    Could you now simplify \[4\sqrt{45}\]just for a little bit more practice?

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