Every rational number is
a natural number
an integer
a real number
a whole number
Between two rational numbers
there is no rational number
there is exactly one rational number
there are infinitely many rational numbers
there are only rational numbers and no irrational numbers
Decimal representation of a rational number cannot be
terminating
non-terminating
non-terminating repeating
non-terminating non-repeating
The product of any two irrational numbers is
always an irrational number
always a rational number
always an integer
sometimes rational, sometimes irrational
The decimal expansion of the number \(\sqrt{2}\) is
a finite decimal
\(1.41421\)
non-terminating recurring
non-terminating non-recurring
Which of the following is irrational?
\(\sqrt{\dfrac{4}{9}}\)
\(\dfrac{\sqrt{12}}{\sqrt{3}}\)
\(\sqrt{7}\)
\(\sqrt{81}\)
Which of the following is irrational?
\(0.14\)
\(0.14\overline{16}\)
\(0.\overline{1416}\)
\(0.4014001400014\ldots\)
A rational number between \(\sqrt{2}\) and \(\sqrt{3}\) is
\(\dfrac{\sqrt{2}+\sqrt{3}}{2}\)
\(\dfrac{\sqrt{2}\cdot\sqrt{3}}{2}\)
\(1.5\)
\(1.8\)
The value of \(1.999\ldots\) in the form \(\dfrac{p}{q}\), where \(p\) and \(q\) are integers and \(q\neq 0\), is
\(\dfrac{19}{10}\)
\(\dfrac{1999}{1000}\)
\(2\)
\(\dfrac{1}{9}\)
\(2\sqrt{3}+\sqrt{3}\) is equal to
\(2\sqrt{6}\)
\(6\)
\(3\sqrt{3}\)
\(4\sqrt{6}\)
\(\sqrt{10}\times\sqrt{15}\) is equal to
\(6\sqrt{5}\)
\(5\sqrt{6}\)
\(\sqrt{25}\)
\(10\sqrt{5}\)
The number obtained on rationalising the denominator of \(\dfrac{1}{\sqrt{7}-2}\) is
\(\dfrac{\sqrt{7}+2}{3}\)
\(\dfrac{\sqrt{7}-2}{3}\)
\(\dfrac{\sqrt{7}+2}{5}\)
\(\dfrac{\sqrt{7}+2}{45}\)
\(\dfrac{1}{\sqrt{9}-\sqrt{8}}\) is equal to
\(\dfrac{1}{2}(3-2\sqrt{2})\)
\(\dfrac{1}{3+2\sqrt{2}}\)
\(3-2\sqrt{2}\)
\(3+2\sqrt{2}\)
After rationalising the denominator of \(\dfrac{7}{3\sqrt{3}-2\sqrt{2}}\), we get the denominator as
\(13\)
\(19\)
\(5\)
\(35\)
The value of \(\dfrac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}\) is equal to
\(\sqrt{2}\)
\(2\)
\(4\)
\(8\)
If \(\sqrt{2}=1.4142\), then \(\sqrt{\dfrac{\sqrt{2}-1}{\sqrt{2}+1}}\) is equal to
\(2.4142\)
\(5.8282\)
\(0.4142\)
\(0.1718\)
\(\sqrt[4]{\sqrt[3]{2^{2}}}\) equals
\(2^{-\frac{1}{6}}\)
\(2^{-6}\)
\(2^{\frac{1}{6}}\)
\(2^{6}\)
The product \(\sqrt[3]{2}\cdot\sqrt[4]{2}\cdot\sqrt[12]{32}\) equals
\(\sqrt{2}\)
\(2\)
\(\sqrt[12]{2}\)
\(\sqrt[12]{32}\)
Value of \(\sqrt[4]{(81)^{-2}}\) is
\(\dfrac{1}{9}\)
\(\dfrac{1}{3}\)
\(9\)
\(\dfrac{1}{81}\)
Value of \((256)^{0.16}\times(256)^{0.09}\) is
\(4\)
\(16\)
\(64\)
\(256.25\)
Which of the following is equal to \(x\)?
\(x^{\frac{12}{7}}-x^{\frac{5}{7}}\)
\(\sqrt[12]{\left(x^{4}\right)^{\frac{1}{3}}}\)
\(\left(\sqrt{x^{3}}\right)^{\frac{2}{3}}\)
\(x^{\frac{12}{7}}\times x^{\frac{7}{12}}\)