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MrRa [10]
3 years ago
11

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 chal

lenge, can you help me out?

Mathematics
1 answer:
scoundrel [369]3 years ago
5 0
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. <span>√4 = 2, rational.</span>

√4 + <span>√16 = 2 + 4 = 6. rational
</span>√5 + √36...<span> irrational
</span>√9 + <span>√24... irrational
</span>2 × <span>√4 = 2 × 2 = 4. rational
</span>√49 × <span>√81 = 7 × 9 = 63. rational
</span>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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