MCQ
$\frac{1}{\sqrt{2}}$ is :
- AA fraction.
- BA rational number.
- ✓An irrational number.
- DNone of these.
✓
Answer
Correct option: C.
An irrational number.
An irrational number is a number that is non $-$ terminating and non $-$ repeating.
$\frac{1}{\sqrt{2}}=\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}} ... ($Rationalising the denominator$)$
$=\frac{\sqrt{2}}{2}$
$=\frac{1}2{}\times\sqrt{2}$
Now, $\frac{1}2{}$ is rational but $\sqrt2$ is irrational.
Product of a rational number and an irrational number is irrational.
Hence, $\frac{1}{\sqrt2}$ is an irrational number.
$\frac{1}{\sqrt{2}}=\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}} ... ($Rationalising the denominator$)$
$=\frac{\sqrt{2}}{2}$
$=\frac{1}2{}\times\sqrt{2}$
Now, $\frac{1}2{}$ is rational but $\sqrt2$ is irrational.
Product of a rational number and an irrational number is irrational.
Hence, $\frac{1}{\sqrt2}$ is an irrational number.
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