Show that $x$ is irrational, if $x^2 = 6.$
View full solution →Question types
Rational and Irrational Numbers question types
142 questions across 6 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
142
Questions
6
Question groups
5
Question types
01
[1 Mark Question Answer]
27 Q→02[2 Mark Question Answer]
63 Q→03[3 marks sum]
15 Q→04[4 marks sum]
17 Q→05[5 marks sum]
12 Q→06TRUE / FALSE
8 Q→Sample Questions
Rational and Irrational Numbers questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $m=\frac{1}{3-2 \sqrt{2}}$ and $n=\frac{1}{3+2 \sqrt{2}}$, find $mn$
View full solution →If $x=\frac{\sqrt{5}-2}{\sqrt{5}+2}$ and $y=\frac{\sqrt{5}+2}{\sqrt{5}-2}$; find : $x^2+y^2+x y$
View full solution →If $x=\frac{\sqrt{5}-2}{\sqrt{5}+2}$ and $y=\frac{\sqrt{5}+2}{\sqrt{5}-2} ;$ find : $x y$
View full solution →Write the lowestrationalising factor of :$3\sqrt2 + 2\sqrt3$
View full solution →Draw a line segment of length $\sqrt{8} \mathrm{~cm}$.
View full solution →Show that Negative of an irrational number is irrational.
Simplify : $\frac{\sqrt{18}}{5 \sqrt{18}+3 \sqrt{72}-2 \sqrt{162}}$
View full solution →Show that $x$ is rational, if $x^2 = 16.$
View full solution →Show that $x $ is rational, if $x^2 = 0.0004.$
View full solution →Draw a line segment of length $\sqrt{3} \mathrm{~cm}$.
View full solution →Show that the product of a non$-$zero rational number and an irrational number is an irrational number.
View full solution →Simplify$:\frac{\sqrt{x^2+y^2}-y}{x-\sqrt{x^2-y^2}} \div \frac{\sqrt{x^2-y^2}+x}{\sqrt{x^2+y^2}+y}$
View full solution →Show that$: x^2+\frac{1}{x^2}=34$, if $\mathrm{x}=3+2 \sqrt{2}$
View full solution →Show that: $\frac{3 \sqrt{2}-2 \sqrt{3}}{3 \sqrt{2}+2 \sqrt{3}}+\frac{2 \sqrt{3}}{\sqrt{3}-\sqrt{2}}=11$
View full solution →Draw a line segment of length $\sqrt{5} \mathrm{~cm}$.
View full solution →Evaluate, correct to one place of decimal, the expression$\frac{5}{\sqrt{20}-\sqrt{10}}$, if $\sqrt{5}=2.2$ and $\sqrt{10}=3.2$
View full solution →Show that: $x^3+\frac{1}{x^3}=52$, if $\mathrm{x}=2+\sqrt{3}$
View full solution →If $x=1-\sqrt{2 } $, find the value of $\left(x-\frac{1}{x}\right)^3$
View full solution →Show that:$\frac{1}{3-2 \sqrt{ } 2}-\frac{1}{2 \sqrt{ } 2-\sqrt{ } 7}+\frac{1}{\sqrt{ } 7-\sqrt{ } 6}-\frac{1}{\sqrt{ } 6-\sqrt{ } 5}+\frac{1}{\sqrt{ } 5-2}=5$
View full solution →Show that: $\frac{4-\sqrt{5}}{4+\sqrt{5}}+\frac{2}{5+\sqrt{3}}+\frac{4+\sqrt{5}}{4-\sqrt{5}}+\frac{2}{5-\sqrt{3}}=\frac{52}{11}$
View full solution →If $x=\sqrt{3}-\sqrt{2}$, find the value of:$(i) x+\frac{1}{x},(ii) x^2+\frac{1}{x^2},(iii)x^3+\frac{1}{x^3},(iv) x^3+\frac{1}{x^3}-3\left(x^2+\frac{1}{x^2}\right)+x+\frac{1}{x}$
View full solution →Using the following figure, show that $BD =\sqrt{x}$.
View full solution →If $\frac{2+\sqrt{ } 5}{2-\sqrt{ } 5}=x$ and $\frac{2-\sqrt{ } 5}{2+\sqrt{ } 5}=y ;$ find the value of $x^2-y^2$
View full solution →Rationalise the denominator of $: \frac{1}{\sqrt{3 } -\sqrt{2 } +1}$
View full solution →Some real numbers are rational numbers.
All real numbers are rational numbers.
All rational numbers are real numbers.
$\frac{5}{11}$ is a rational number.
View full solution →$\frac{2}{7}$ ia an irrational number.
View full solution →Generate a Rational and Irrational Numbers paper free
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