Mathematics
Irrational numbers
Practice questions
If (a) and (b) are positive integers and (\sqrt{a}+\sqrt{b}) is rational, while (a) is not a perfect square, which conclusion about (b) can definitely be true?Which option gives the correct value of (\frac{\sqrt{45}+\sqrt{20}}{\sqrt{5}})?If (x=\sqrt{7}+\sqrt{28}), what is the value of (\frac{x^2}{7})?Which statement is correct for (\sqrt{5}+\sqrt{20}-\sqrt{45})?If (p) is a prime number, which main idea is used to prove that (\sqrt{p}) is irrational?Which option correctly describes the nature of ((\sqrt{11}+\sqrt{3})(\sqrt{11}-\sqrt{3}))?If (x=\frac{1}{\sqrt{6}-\sqrt{5}}), what is (x) equal to?Which given decimal is definitely irrational?If (x=\sqrt{3}+\sqrt{2}), which is the rationalized form of (\frac{1}{x})?Which option makes the sum of two irrational numbers rational?If (a=\sqrt{8}+\sqrt{18}) and (b=\sqrt{8}-\sqrt{18}), what is the value of (ab)?Which option is the correct simplified form of (\sqrt{50}+\sqrt{72}-\sqrt{98})?If (\sqrt{m}+\sqrt{n}=5) and (m,n) are positive integers, which pair is possible?Which number is an irrational number between (1) and (2), but greater than (\sqrt{2})?If (x=\sqrt{10}-\sqrt{2}), what is (x^2) equal to?Which option helps identify (2\sqrt{3}+3\sqrt{2}) as a square of a surd expression?Which option is equal to (5+2\sqrt{6})?If (x=\sqrt{a}) is irrational and (a<50) is a positive integer, which (a) is not suitable?In which option is the number irrational and its reciprocal also irrational?If (x=\sqrt{2}+\sqrt{5}) and (y=\sqrt{5}-\sqrt{2}), what is the value of (xy)?