(B) To rationalise the denominator of $\frac{3+\sqrt{2}}{4 \sqrt{2}}$,we multiply both the numerator and the denominator by $\sqrt{2}$:$\frac{3+\sqrt{

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(B) To rationalise the denominator of $\frac{3+\sqrt{2}}{4 \sqrt{2}}$,we multiply both the numerator and the denominator by $\sqrt{2}$:$\frac{3+\sqrt{2}}{4 \sqrt{2}} = \frac{3+\sqrt{2}}{4 \sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$$= \frac{\sqrt{2}(3+\sqrt{2})}{4 \times (\sqrt{2} \times \sqrt{2})}$$= \frac{3 \sqrt{2} + 2}{4 \times 2}$$= \frac{3 \sqrt{2} + 2}{8}$

Class 9 Mathematics Number Systems Mix Examples - Number Systems

Difficult

Rationalise the denominator of the following:
$\frac{3+\sqrt{2}}{4 \sqrt{2}}$

A
$\frac{3 \sqrt{2}+2}{7}$
B
$\frac{3 \sqrt{2}+2}{8}$
C
$\frac{3 \sqrt{2}+2}{5}$
D
$\frac{3 \sqrt{7}+2}{3}$

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Mix Examples - Number Systems

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0.$
$0.\overline{125}$

Medium

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Fill in the blanks to make the following statement true: The decimal expansion of $\frac{47}{50}$ is of $\ldots \ldots \ldots$ type.

Easy

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For each question,select the proper option from four options given,to make the statement true: $4 . \overline{185} = \ldots \ldots$

Medium

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Prove that $(1^{3}+2^{3}+3^{3}+4^{3}+5^{3})^{\frac{1}{2}} = (1^{3}+2^{3}+3^{3}+4^{3})^{\frac{1}{2}} + (5^{3})^{\frac{1}{3}}$.

Difficult

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Classify the following numbers as rational or irrational with justification:
$(i)$ $\sqrt{196}$
$(ii)$ $3\sqrt{18}$

Medium

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Rationalise the denominator of the following:$\frac{3+\sqrt{2}}{4 \sqrt{2}}$

Similar Questions

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0.$$0.\overline{125}$

Fill in the blanks to make the following statement true: The decimal expansion of $\frac{47}{50}$ is of $\ldots \ldots \ldots$ type.

For each question,select the proper option from four options given,to make the statement true: $4 . \overline{185} = \ldots \ldots$

Prove that $(1^{3}+2^{3}+3^{3}+4^{3}+5^{3})^{\frac{1}{2}} = (1^{3}+2^{3}+3^{3}+4^{3})^{\frac{1}{2}} + (5^{3})^{\frac{1}{3}}$.

Classify the following numbers as rational or irrational with justification:$(i)$ $\sqrt{196}$$(ii)$ $3\sqrt{18}$

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Rationalise the denominator of the following:
$\frac{3+\sqrt{2}}{4 \sqrt{2}}$

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0.$
$0.\overline{125}$

Classify the following numbers as rational or irrational with justification:
$(i)$ $\sqrt{196}$
$(ii)$ $3\sqrt{18}$