1. (2√5)/5
2. -44√7
3. 8√17
4. -6√3+12
For 1: Multiply the numerator and denominator by √5:
[tex]\frac{2}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{2\sqrt{5}}{5}[/tex]
For 2: Simplify √112:
√112 = √(2*56) = √(2*2*28) = √(4*4*7) = 2*2√7 = 4√7
Now multiply by the -11 coefficient:
-11(4√7) = -44√7
For 3: Add the radicals as you would variables that are like terms.
For 4: Multiply by the conjugate. The conjugate of the denominator has the same values with the sign of the radical changed:
[tex]\frac{6}{\sqrt{3}+2}\times \frac{\sqrt{3}-2}{\sqrt{3}-2}=\frac{6(\sqrt{3}-2)}{(\sqrt{3}+2)(\sqrt{3}-2)}
\\
\\=\frac{6\sqrt{3}-6*2}{\sqrt{3}*\sqrt{3}-2\sqrt{3}+2\sqrt{3}-2*2}
\\
\\=\frac{6\sqrt{3}-12}{3-4}=\frac{6\sqrt{3}-12}{-1}=-6\sqrt{3}+12[/tex]
