Mathematics
Irrational numbers
Practice questions
Which option is equal to ((\sqrt{7}+\sqrt{2})^2-(\sqrt{7}-\sqrt{2})^2)?If (x=\sqrt{6}+\sqrt{2}) and (y=\sqrt{6}-\sqrt{2}), what is the simplified form of (\frac{x}{y})?Which given number is smaller than (2\sqrt{3}) and greater than (\sqrt{11})?If (x=\sqrt{2}), what is the value of (x^4-4x^2+4)?Which option is a wrong step in the proof of irrationality of (\sqrt{2})?If (a=1+\sqrt{5}), what is the value of (a^2-2a)?Which option gives the simplified form of (\sqrt{48}+\sqrt{75}-\sqrt{27})?If (x=\sqrt{3}+\sqrt{2}), what is the value of ((x-\sqrt{3})(x-\sqrt{2}))?Which option is the correct simplified form of (\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32})?If (x=\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}), what is the value and nature of (x)?If (x=\frac{\sqrt{10}+\sqrt{6}}{\sqrt{10}-\sqrt{6}}), what is the simplified form of (x)?If (x=\sqrt{5}+\sqrt{2}) and (y=\sqrt{5}-\sqrt{2}), what is the value of (x^2+y^2)?Which option gives the correct value of (\frac{\sqrt{12}+\sqrt{27}}{\sqrt{3}})?If (\sqrt{m}+\sqrt{n}=7) and (m,n) are positive integers, which pair is definitely possible?If (x=2+\sqrt{3}), what is the value of (x^2+\frac{1}{x^2})?Which option correctly describes the nature of (0.303003000300003\ldots)?If (a=\sqrt{6}+\sqrt{2}) and (b=\sqrt{6}-\sqrt{2}), what is the value of (a^2-b^2)?In which option is (x) irrational but (x+\frac{1}{x}) rational?Which option is the correct simplified form of (\sqrt{18}+\sqrt{50}-\sqrt{8})?If (x=\sqrt{7}-\sqrt{3}), what is (x^2) equal to?