R S Aggarwal and Veena Aggarwal Solutions for Exercise 9: VERY-SHORT-ANSWER QUESTIONS

What can you say about the sum of a rational number and an irrational number?

Simplify and give the answer in $\frac{p}{q}$ form: ${\left(\frac{3125}{243}\right)}^{\frac{4}{5}}$

Give an example of two irrational numbers whose sum as well as product is rational.

Is the product of a rational and an irrational number always irrational? Give an example.

Give an example of a number $x$ such that $x^2$ is an irrational number and $x^3$ is a rational number.

If the simplified form of $(2\sqrt{5}+3\sqrt{2}{)}^2$ is $38+\sqrt{x}$ then, write the value of $x$ as final answer.

If $\frac{2^n+2^{n-1}}{2^{n+1}-2^n}=\frac{m}{n}$, then find the value of $m+n$.

Simplify: ${\left[{\left\{(256{)}^{-\frac{1}{2}}\right\}}^{-\frac{1}{4}}\right]}^2$