Fill in the blanks to make the following statement true: $\sqrt{7}$ is a/an $\ldots \ldots \ldots$ number.
(IRRATIONAL) number is called irrational if it cannot be written in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$. Since $7$ is not a perfect square,its square root,$\sqrt{7}$,is an irrational number.
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Similar Questions
Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three decimal places.
$\frac{1}{\sqrt{3}+\sqrt{2}}$
$\frac{1}{\sqrt{3}+\sqrt{2}}$
Medium
View SolutionClassify the following numbers as rational or irrational with justification:
$(i)$ $-\sqrt{0.4}$
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$
$(i)$ $-\sqrt{0.4}$
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$
Medium
View SolutionSimplify the following expression: $(\sqrt{15}+\sqrt{7})(\sqrt{15}-\sqrt{7})$
Easy
View SolutionExpress $0.12 \overline{3}$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.
Medium
View SolutionFind the value of $a$ :
$\frac{5+2 \sqrt{3}}{7+4 \sqrt{3}}=a-6 \sqrt{3}$
$\frac{5+2 \sqrt{3}}{7+4 \sqrt{3}}=a-6 \sqrt{3}$
Difficult
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