Rationalise the denominator of $\frac{1}{\sqrt{2}}$.
Rationalise the denominator of $\frac{1}{\sqrt{2}}$.
We want to write $\frac{1}{\sqrt{2}}$ as an equivalent expression in which the denominator is a rational number. We know that $\sqrt{2} \cdot \sqrt{2}$ is rational. We also know that multiplying $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ will give us an equivalent expression, since $\frac{\sqrt{2}}{\sqrt{2}}=1 .$ So, we put these two facts together to get
$\frac{1}{\sqrt{2}}=\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}$
In this form, it is easy to locate $\frac{1}{\sqrt{2}}$ on the number line. It is half way between $0$ and $\sqrt{2}$.
Similar Questions
Show that $3.142678$ is a rational number. In other words, express $3.142678$ in the form $\frac {p }{q }$, where $p$ and $q$ are integers and $q \ne 0$.
Show that $3.142678$ is a rational number. In other words, express $3.142678$ in the form $\frac {p }{q }$, where $p$ and $q$ are integers and $q \ne 0$.
Rationalise the denominator of $\frac{1}{7+3 \sqrt{2}}$
Rationalise the denominator of $\frac{1}{7+3 \sqrt{2}}$
Rationalise the denominators of the following :
$(i)$ $\frac{1}{\sqrt{7}}$
$(ii)$ $\frac{1}{\sqrt{7}-\sqrt{6}}$
$(iii)$ $\frac{1}{\sqrt{5}+\sqrt{2}}$
$(iv)$ $\frac{1}{\sqrt{7}-2}$
Rationalise the denominators of the following :
$(i)$ $\frac{1}{\sqrt{7}}$
$(ii)$ $\frac{1}{\sqrt{7}-\sqrt{6}}$
$(iii)$ $\frac{1}{\sqrt{5}+\sqrt{2}}$
$(iv)$ $\frac{1}{\sqrt{7}-2}$
Express the following in the form $\frac {p}{q}$, where $p$ and $q$ are integers and $q \ne 0$.
$(i)$ $0 . \overline{6}$
$(ii)$ $0 . 4\overline{7}$
$(iii)$ $0 . \overline{001}$
Express the following in the form $\frac {p}{q}$, where $p$ and $q$ are integers and $q \ne 0$.
$(i)$ $0 . \overline{6}$
$(ii)$ $0 . 4\overline{7}$
$(iii)$ $0 . \overline{001}$
Write three numbers whose decimal expansions are non-terminating non-recurring.
Write three numbers whose decimal expansions are non-terminating non-recurring.