Mathematics
Irrational numbers
Practice questions
Which number is the simplified form of (\sqrt{27}+\sqrt{12})?If (\sqrt{2}) is written as (\frac{p}{q}), where (p) and (q) are coprime, what contradiction appears in the proof?Which option gives the correct simplified form and nature of (\sqrt{32}-\sqrt{2})?If (x=\sqrt{11}+\sqrt{44}), what is the simplified form and nature of (x)?Which option gives a rational decimal even though it does not terminate?If (a=\sqrt{3}+2) and (b=\sqrt{3}-2), what is the nature of (ab)?Which of the following expressions is definitely irrational?If (\frac{5}{\sqrt{k}}) is irrational and (k) is a positive integer, which (k) is possible?Which option is an example of two different irrational numbers whose quotient is rational?If (x=4+\sqrt{6}), what will be the nature of (x-4)?If (r) is a non-zero rational number and (x) is an irrational number, which statement about (\frac{x}{r}) is correct?Which option gives the correct simplified form and nature of (\sqrt{2}+\sqrt{18})?Which of the following decimals represents an irrational number?If (x=\sqrt{3}+2), what will be the value and nature of (x-\sqrt{3})?In which option is the given number definitely irrational?If (\sqrt{n}) is rational when (n) is a positive integer, what is the correct decision for (n=72)?If (a=5+\sqrt{7}) and (b=5-\sqrt{7}), what is the value of (ab)?Which number is an irrational number between (3) and (4)?If (\frac{1}{x}) is rational and (x\neq0), what is the correct conclusion about (x) being irrational?Which option is the rationalized form of (\frac{3}{2+\sqrt{5}})?