Question

write true or false
a) if p and q are perfect squares, then square root of p devided by q is a rational number.
b) the square root of a prime number is not a rational number.

Answer 1

$$\begin{gathered} \left(\mathrm{a}\right).\mathrm{True} \\ \mathbf{EXPLANATION}\mathbf{}\mathbf{:} \\ \mathrm{Let}\mathrm{p}=4\mathrm{and}\mathrm{q}=9 \\ \mathrm{Now},\sqrt{\mathrm{p}}=2\mathrm{and}\sqrt{\mathrm{q}}=3 \\ \mathrm{Now},\frac{\sqrt{\mathrm{p}}}{\sqrt{\mathrm{q}}}=\frac{2}{3},\mathrm{a}\mathrm{rational}\mathrm{number} \\ \left(\mathrm{b}\right).\mathrm{True} \\ \mathbf{EXPLANATION}\mathbf{}\mathbf{:} \\ \mathrm{Consider}\mathrm{a}\mathrm{prime}\mathrm{number}2. \\ \mathrm{Now},\sqrt{2}\mathrm{is}\mathrm{an}\mathrm{irrational}\mathrm{number}. \\ \mathrm{So},\mathrm{square}\mathrm{root}\mathrm{of}\mathrm{a}\mathrm{prime}\mathrm{number}\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{rational}\mathrm{number}. \end{gathered}$$