Mathematics
Irrational numbers
Practice questions
Which option is the correct value of (\frac{\sqrt{75}-\sqrt{12}}{\sqrt{3}})?If (x=\sqrt{5}-2), what is the value of (x+\frac{1}{x})?Which option is a correct pair of two irrational numbers between (2) and (3)?If (a=\sqrt{3}+\sqrt{2}) and (b=\sqrt{3}-\sqrt{2}), what is the value of (\frac{a-b}{a+b})?In which option is (\sqrt{a}+\sqrt{b}) irrational but ((\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})) rational?If (x=\sqrt{2}+\sqrt{5}), what is the value of ((x-\sqrt{2})^2)?Which option correctly gives the reciprocal of (\sqrt{2}+\sqrt{3})?If (x=1+\sqrt{2}+\sqrt{3}), what is the nature of (x-1)?Which option is the correct simplified form of (\sqrt{96}-\sqrt{54}+\sqrt{24})?If (x=\sqrt{3}+\sqrt{5}) and (y=\sqrt{5}+\sqrt{7}), what is the nature of (y-x)?Which option is correct about (3+\sqrt{2}) and (3-\sqrt{2})?If (x=\sqrt{2}), which statement about (\frac{x^6-8}{x^2-2}) is correct?Which option correctly gives the difference between (\sqrt{45}) and (2\sqrt{5})?If (x=\sqrt{5}+\sqrt{2}), what is the value of ((x^2-7)^2)?In which option is (\sqrt{p}) irrational and (p) also prime?If (x=4+\sqrt{15}) and (y=4-\sqrt{15}), what is the value of (x^2+y^2)?Which option helps show that the claim (\sqrt{2}+\sqrt{3}+\sqrt{6}) is rational is false?If (x=\sqrt{7}+2), what is the value of ((x-2)(x+2))?Which option is the correct simplified form of (\sqrt{2}+\sqrt{18}-\sqrt{50}+\sqrt{98})?If (x=\sqrt{6}+\sqrt{5}), what is the value and nature of (x^3+\frac{1}{x^3})?