Mathematics
Irrational numbers
Practice questions
Which option disproves the wrong idea (\sqrt{a}+\sqrt{b}=\sqrt{a+b})?In which option is (\frac{\sqrt{a}}{\sqrt{b}}) irrational?Which option correctly describes the nature of (\frac{\sqrt{18}}{\sqrt{5}})?If (x=2+\sqrt{3}), what is the value of (x+\frac{1}{x})?If (x=3+\sqrt{8}), which statement about the nature and simplified form of (x) is correct?Which option explains why (\sqrt{2}+\sqrt{3}) is irrational?If (x=\sqrt{5}+\sqrt{3}), what is the value of (x-\frac{2}{x})?Which option makes (\sqrt{a}+\sqrt{b}) irrational?If (x=\sqrt{2}+\sqrt{7}), what is the value of (x^2-9)?Which option correctly states the relation between (\sqrt{3}) and (\sqrt{12})?If (x=\sqrt{3}-1), what is the value of ((x+1)^2)?Which option correctly tells which is greater between (2\sqrt{3}) and (3\sqrt{2})?If (x=2\sqrt{5}) and (y=5\sqrt{2}), what is the nature of (xy)?Which option is correct for (0.10110111011110\ldots), where the number of (1)'s increases at each stage?If (x=\sqrt{13}+2), what is the value of (x^2-4x)?Which option is equal to the simplified form of (\frac{2+\sqrt{3}}{2-\sqrt{3}})?If (a=7+4\sqrt{3}), which option represents a square root of (a)?Which option gives the correct simplified form of (\sqrt{80}-\sqrt{45}+\sqrt{20})?Which option is the correct simplified form of (\sqrt{80}-\sqrt{45}+\sqrt{20})?If (x) is irrational and (x+\sqrt{2}) is rational, which can be a possible form of (x)?