State whether the following statements are true or false? Justify your answer.
$(i)$ $\frac{\sqrt{2}}{3}$ is a rational number.
$(ii)$ There are infinitely many integers between any two integers.
State whether the following statements are true or false? Justify your answer.
$(i)$ $\frac{\sqrt{2}}{3}$ is a rational number.
$(ii)$ There are infinitely many integers between any two integers.
$(i)$ The given statement is false. $\frac{\sqrt{2}}{3}$ is of the form $\frac{p}{q}$ but $p=\sqrt{2}$ is not an integer.
$(ii)$ The given statement is false. Consider two integers $3$ and $4 .$ There is no integers between $3$ and $4 .$
Similar Questions
Rationalise the denominator in each of the following
$\frac{5-2 \sqrt{6}}{5+2 \sqrt{6}}$
Rationalise the denominator in each of the following
$\frac{5-2 \sqrt{6}}{5+2 \sqrt{6}}$
Insert a rational number and an irrational number between the following:
$0.0001$ and $0.001$
Insert a rational number and an irrational number between the following:
$0.0001$ and $0.001$
Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ upto three places of decimal.
$\frac{4}{\sqrt{3}}$
Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ upto three places of decimal.
$\frac{4}{\sqrt{3}}$
Represent $\sqrt{5}$ on the number line.
Represent $\sqrt{5}$ on the number line.
Find which of the variables $x, y, z$ and $u$ represent rational numbers and which irrational numbers:
$(i)$ $x^{2}=5$
$(ii)$ $\quad y^{2}=9$
$(iii)$ $z^{2}=.04$
$(iv)$ $u^{2}=\frac{17}{4}$
Find which of the variables $x, y, z$ and $u$ represent rational numbers and which irrational numbers:
$(i)$ $x^{2}=5$
$(ii)$ $\quad y^{2}=9$
$(iii)$ $z^{2}=.04$
$(iv)$ $u^{2}=\frac{17}{4}$