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I need help with this Algebra 1 Study Guide. It has 5 questions . This has many hard questions so to you people that like a challenge, can you help me out?

I need help with this Algebra 1 Study Guide. It has 5 questions . This has many hard questions so to you people that like a challenge, can you help me out? class=
I need help with this Algebra 1 Study Guide. It has 5 questions . This has many hard questions so to you people that like a challenge, can you help me out? class=
I need help with this Algebra 1 Study Guide. It has 5 questions . This has many hard questions so to you people that like a challenge, can you help me out? class=
I need help with this Algebra 1 Study Guide. It has 5 questions . This has many hard questions so to you people that like a challenge, can you help me out? class=
I need help with this Algebra 1 Study Guide. It has 5 questions . This has many hard questions so to you people that like a challenge, can you help me out? class=

Verified Answer :

RedRicin
  1. Rational numbers can be written as a ratio (fraction)
    Whole numbers are rational. 5 = 5/1, for example.
    Square roots are NOT rational.  Example: √3
    However, square roots of square numbers can be simplified, and are therefore rational. √4 = 2, rational.

    √4 + √16 = 2 + 4 = 6. rational
    √5 + √36... irrational
    √9 + √24... irrational
    2 × √4 = 2 × 2 = 4. rational
    √49 × √81 = 7 × 9 = 63. rational
    3√12... irrational

    2. \(n^\frac12=\sqrtn\)
    \(9^\frac32=9^3\times\frac12=\sqrt{9^3}=\sqrt{729}=29\)

    3. \(\frac{n^a}{n^b}=n^{a-b}\)

    \(\frac{a^\frac13}{a^\frac14}=a^{\frac13-\frac14}=a^{\frac{1}{12}}\)

    4. \(n^\frac1x=\sqrt[x]n\)

    \(\sqrt[3]{m^2n^5}=m^{\frac23}n^{\frac53}\)

    5. \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\)

    \(\sqrt{3}\times\sqrt{12}=\sqrt{3\times12}=\sqrt{36}=6\)

    A, since neither 3 nor 12 is a square but we end up with 6.

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