Mathematics
Irrational numbers
Practice questions
Which option is the simplified form of (\sqrt{2}+\sqrt{8}+\sqrt{32}+\sqrt{128})?If (p) and (q) are coprime integers and (\sqrt{5}=\frac{p}{q}) is assumed, in what form does the contradiction appear?Which option correctly compares (4\sqrt{3}) and (3\sqrt{5})?If (x=\sqrt{11}+\sqrt{7}), what is the value of (x^2-18)?In which option do two irrational numbers have a rational product but an irrational sum?If (x=\frac{\sqrt{3}}{\sqrt{2}}), which statement about (x^2) and (x) is correct?Which option is the rationalized form of (\frac{1}{\sqrt{5}+\sqrt{2}})?If (a=\sqrt{2}+\sqrt{3}+\sqrt{5}), which irrational term must appear in (a^2)?In which option is (\sqrt{a}+\sqrt{b}) rational?If (x=\sqrt{3}+\sqrt{2}), what is the value of (x^4-10x^2+1)?Which option makes (\sqrt{a}\times\sqrt{b}) irrational?If (x=5-\sqrt{24}), which is the correct form of (\frac{1}{x})?Which given statement is correct?If (x=\sqrt{8}+\sqrt{18}), what is the value of (\frac{x}{\sqrt{2}})?Which option gives the correct comparison between (\sqrt{3}+\sqrt{6}) and (\sqrt{12})?If (a=3+\sqrt{5}), what is the value of (a^2-6a)?Which option is correct for (1.202002000200002\ldots)?If (x=\sqrt{13}+\sqrt{12}), what is the value of (x\cdot(\sqrt{13}-\sqrt{12}))?In which option is (\sqrt{a}-\sqrt{b}) rational while the two square roots are different?If (x=\sqrt{2}+\sqrt{3}), what is the value of (x^2-2\sqrt{6})?