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) $ $125^{\frac{1}{3}}$
$(i)$ $(64)^{\frac{1}{2}}=\left(8^{2}\right)^{\frac{1}{2}}=8^{2 \times \frac{1}{2}}=8$
$(ii)$ $32^{\frac{1}{5}}=\left(2^{5}\right)^{\frac{1}{5}}=2^{5 \times \frac{1}{5}}=2^{1}=2$
$(iii)$ $125^{\frac{1}{3}}=\left(5^{3}\right)^{\frac{1}{3}}=5^{3 \times \frac{1}{3}}=5$
Similar Questions
Classify the following numbers as rational or irrational :
$(i)$ $2-\sqrt{5}$
$(ii)$ $(3+\sqrt{23})-\sqrt{23}$
$(iii)$ $\frac{2 \sqrt{7}}{7 \sqrt{7}}$
$(iv)$ $\frac{1}{\sqrt{2}}$
$(v)$ $2 \pi$
Classify the following numbers as rational or irrational :
$(i)$ $2-\sqrt{5}$
$(ii)$ $(3+\sqrt{23})-\sqrt{23}$
$(iii)$ $\frac{2 \sqrt{7}}{7 \sqrt{7}}$
$(iv)$ $\frac{1}{\sqrt{2}}$
$(v)$ $2 \pi$
Show that $1.272727 \ldots=1 . \overline{27}$ . can be expressed in the form $\frac {p }{q }$, where $p$ and $q$ are integers and $q \ne 0$.
Show that $1.272727 \ldots=1 . \overline{27}$ . can be expressed in the form $\frac {p }{q }$, where $p$ and $q$ are integers and $q \ne 0$.
Show that $0.2353535 \ldots=0.2 \overline{35}$ can be expressed in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.
Show that $0.2353535 \ldots=0.2 \overline{35}$ can be expressed in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.
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.
State whether the following statements are true or false. Justify your answers.
$(i)$ Every irrational number is a real number.
$(ii)$ Every point on the number line is of the form $\sqrt m$ , where $m$ is a natural number.
$(iii)$ Every real number is an irrational number.
State whether the following statements are true or false. Justify your answers.
$(i)$ Every irrational number is a real number.
$(ii)$ Every point on the number line is of the form $\sqrt m$ , where $m$ is a natural number.
$(iii)$ Every real number is an irrational number.