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)}
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\\=\frac{6\sqrt{3}-6*2}{\sqrt{3}*\sqrt{3}-2\sqrt{3}+2\sqrt{3}-2*2}
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\\=\frac{6\sqrt{3}-12}{3-4}=\frac{6\sqrt{3}-12}{-1}=-6\sqrt{3}+12[/tex]