Question

1. Simplify 2/radical 5

Answer 1

1.  (2√5)/5
2.  -44√7
3.  8√17
4.  -6√3+12

For 1:  Multiply the numerator and denominator by √5:
$\frac{2}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{2\sqrt{5}}{5}$

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:
$\frac{6}{\sqrt{3}+2}\times \frac{\sqrt{3}-2}{\sqrt{3}-2}=\frac{6(\sqrt{3}-2)}{(\sqrt{3}+2)(\sqrt{3}-2)} \\ \\=\frac{6\sqrt{3}-6*2}{\sqrt{3}*\sqrt{3}-2\sqrt{3}+2\sqrt{3}-2*2} \\ \\=\frac{6\sqrt{3}-12}{3-4}=\frac{6\sqrt{3}-12}{-1}=-6\sqrt{3}+12$