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. [tex]n^\frac12=\sqrtn[/tex]
[tex]9^\frac32=9^3\times\frac12=\sqrt{9^3}=\sqrt{729}=29[/tex]
3. [tex]\frac{n^a}{n^b}=n^{a-b}[/tex]
[tex] \frac{a^\frac13}{a^\frac14}=a^{\frac13-\frac14}=a^{\frac{1}{12}}[/tex]
4. [tex]n^\frac1x=\sqrt[x]n[/tex]
[tex]\sqrt[3]{m^2n^5}=m^{\frac23}n^{\frac53}[/tex]
5. [tex]\sqrt{a}\times\sqrt{b}=\sqrt{ab}[/tex]
[tex]\sqrt{3}\times\sqrt{12}=\sqrt{3\times12}=\sqrt{36}=6[/tex]
A, since neither 3 nor 12 is a square but we end up with 6.
