Question

The number N = $\frac{(5\sqrt{3}+\sqrt{50})(5-\sqrt{24})}{\sqrt{75}-5\sqrt{2}}$ when simplified reduces to

• A. an irrational number
• B. rational which is not an integer
• C. unity
• D. an even prime

Answer 1

The correct option is C unity

N = $\frac{(5\sqrt{3}+\sqrt{50})(5-\sqrt{24})}{\sqrt{75}-5\sqrt{2}}$
Rationalising,
N = $\frac{(5\sqrt{3}+\sqrt{50})(5-\sqrt{24})(\sqrt{75}+5\sqrt{2})}{(\sqrt{75}-5\sqrt{2})(\sqrt{75}+5\sqrt{2})}$
N = $\frac{{(5\sqrt{3}+\sqrt{50})}^2(5-\sqrt{24})}{(75-50)}$
N = $\frac{{(5\sqrt{3}+\sqrt{50})}^2(5-\sqrt{24})}{(75-50)}$
N = $\frac{(75+50+50\sqrt{6})(5-2\sqrt{6})}{25}$
N = $(5+2\sqrt{6})(5-2\sqrt{6})$
N = $25-24$
N = $1$