State whether the following statements are true or false? Justify your answer.
$(i)$ Number of rational numbers between $15$ and $18$ is finite.
$(ii)$ There are numbers which cannot be written in the form $\frac{p}{q}, q \neq 0, p , q$ both are integers.
State whether the following statements are true or false? Justify your answer.
$(i)$ Number of rational numbers between $15$ and $18$ is finite.
$(ii)$ There are numbers which cannot be written in the form $\frac{p}{q}, q \neq 0, p , q$ both are integers.
$(i)$ The given statement is false. There lies infinitely many rational numbers between any two rational number. Hence, number of rational numbers between $15$ and $18$ are infinite.
$(ii)$ The given statement is true. For example, $\frac{\sqrt{3}}{\sqrt{5}}$ is of the form $\frac{p}{q}$ but $p=\sqrt{3}$ and $q=\sqrt{5}$ are not integers.
Similar Questions
Find three different irrational numbers lying between $\sqrt{3}$ and $\sqrt{5}$.
Find three different irrational numbers lying between $\sqrt{3}$ and $\sqrt{5}$.
Simplify the following:
$\sqrt{45}-3 \sqrt{20}+4 \sqrt{5}$
Simplify the following:
$\sqrt{45}-3 \sqrt{20}+4 \sqrt{5}$
Classify the following numbers as rational or irrational with justification:
$(i)$ $-\sqrt{0.4}$
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$
Classify the following numbers as rational or irrational with justification:
$(i)$ $-\sqrt{0.4}$
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$
Find three rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$.
Find three rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$.
State whether each of the following statements is true or false
Each integer is a whole number.
State whether each of the following statements is true or false
Each integer is a whole number.