Rationalise the denominator of $\frac{1}{2+\sqrt{3}}$.
Rationalise the denominator of $\frac{1}{2+\sqrt{3}}$.
We use the Identity $(iv)$ given earlier. Multiply and divide $\frac{1}{2+\sqrt{3}}$ by
$2-\sqrt{3}$ to get $\frac{1}{2+\sqrt{3}} \times \frac{2-\sqrt{3}}{2-\sqrt{3}}=\frac{2-\sqrt{3}}{4-3}=2-\sqrt{3}$.
Similar Questions
Visualise $3.765$ on the number line, using successive magnification.
Visualise $3.765$ on the number line, using successive magnification.
Express $0.99999 \ldots$ in the form $\frac{p}{q}$. Are you surprised by your answer ? With your teacher and classmates discuss why the answer makes sense.
Express $0.99999 \ldots$ in the form $\frac{p}{q}$. Are you surprised by your answer ? With your teacher and classmates discuss why the answer makes sense.
Find :
$(i)$ $64^{\frac{1}{2}}$
$(ii)$ $32^{\frac{1}{5}}$
$(iii) $ $125^{\frac{1}{3}}$
Find :
$(i)$ $64^{\frac{1}{2}}$
$(ii)$ $32^{\frac{1}{5}}$
$(iii) $ $125^{\frac{1}{3}}$
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 $q \ne 0$.
Find :
$(i)$ $2^{\frac{2}{3}} \cdot 2^{\frac{1}{5}}$
$(ii)$ $\left(\frac{1}{3^{3}}\right)^{7}$
$(iii)$ $\frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}}$
$(iv)$ $7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}}$
Find :
$(i)$ $2^{\frac{2}{3}} \cdot 2^{\frac{1}{5}}$
$(ii)$ $\left(\frac{1}{3^{3}}\right)^{7}$
$(iii)$ $\frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}}$
$(iv)$ $7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}}$