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
In each of the following numbers rationalise the denominator
$\frac{30}{5 \sqrt{3}-3 \sqrt{5}}$
In each of the following numbers rationalise the denominator
$\frac{30}{5 \sqrt{3}-3 \sqrt{5}}$
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:
$(i)$ $-\sqrt{0.4}$
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$
Simplify: $\frac{7 \sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2 \sqrt{5}}{\sqrt{6}+\sqrt{5}}-\frac{3 \sqrt{2}}{\sqrt{15}+3 \sqrt{2}}$
Simplify: $\frac{7 \sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2 \sqrt{5}}{\sqrt{6}+\sqrt{5}}-\frac{3 \sqrt{2}}{\sqrt{15}+3 \sqrt{2}}$
Which of the following is irrational?
Which of the following is irrational?
Simplify the following:
$(\sqrt{3}-\sqrt{2})^{2}$
Simplify the following:
$(\sqrt{3}-\sqrt{2})^{2}$