Rationalise the denominator of $\frac{1}{7+3 \sqrt{2}}$
Rationalise the denominator of $\frac{1}{7+3 \sqrt{2}}$
$\frac{1}{7+3 \sqrt{2}}=\frac{1}{7+3 \sqrt{2}} \times\left(\frac{7-3 \sqrt{2}}{7-3 \sqrt{2}}\right)=\frac{7-3 \sqrt{2}}{49-18}=\frac{7-3 \sqrt{2}}{31}$
Similar Questions
State whether the following statements are true or false. Give reasons for your answers.
$(i)$ Every natural number is a whole number.
$(ii)$ Every integer is a whole number.
$(iii)$ Every rational number is a whole number
State whether the following statements are true or false. Give reasons for your answers.
$(i)$ Every natural number is a whole number.
$(ii)$ Every integer is a whole number.
$(iii)$ Every rational number is a whole 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.
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.
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) $ $125^{\frac{1}{3}}$
Visualise $4. \overline{26}$ . on the number line, up to $4$ decimal places.
Visualise $4. \overline{26}$ . on the number line, up to $4$ decimal places.
Look at several examples of rational numbers in the form $\frac{p}{q}(q \neq 0),$ where $p$ and $q$ are integers with no common factors other than $1$ and having terminating decimal representations (expansions). Can you guess what property $q$ must satisfy ?
Look at several examples of rational numbers in the form $\frac{p}{q}(q \neq 0),$ where $p$ and $q$ are integers with no common factors other than $1$ and having terminating decimal representations (expansions). Can you guess what property $q$ must satisfy ?