Separate the rational and irrational from among the following number:-
$2 . \overline{4}$
View full solution →$2 . \overline{4}$
Question types
Rational and Irrational Numbers question types
318 questions across 7 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
318
Questions
7
Question groups
5
Question types
01
[1 Mark Question Answer]
69 Q→02[2 Mark Question Answer]
107 Q→03[3 marks sum]
84 Q→04[4 marks sum]
1 Q→05[5 marks sum]
5 Q→06TRUE / FALSE
12 Q→07MCQ
40 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.
Separate the rational and irrational from among the following number:-
$\sqrt[3]{5}$
View full solution →$\sqrt[3]{5}$
Separate the rational and irrational from among the following number:-
$\pi$
View full solution →$\pi$
Separate the rational and irrational from among the following number:-
0
0
Separate the rational and irrational from among the following number:-
$-\sqrt{3}$
View full solution →$-\sqrt{3}$
Show that is irrational:
$\frac{6}{\sqrt{3}}$
View full solution →$\frac{6}{\sqrt{3}}$
Show that is irrational:
$(\sqrt{5}+\sqrt{3})^2$
View full solution →$(\sqrt{5}+\sqrt{3})^2$
Show that is irrational:
$(3-\sqrt{3})^2$
View full solution →$(3-\sqrt{3})^2$
Show that is irrational:
$(2+\sqrt{5})^2$
View full solution →$(2+\sqrt{5})^2$
State, giving reason, whether the given number is rational or irrational:
$(3+\sqrt{3})(3-\sqrt{3})$
View full solution →$(3+\sqrt{3})(3-\sqrt{3})$
Find a rational number between $\frac{3}{5}$ and $\frac{7}{9}$.
View full solution →Rationalise the denominator of the following:
$\frac{1}{(2 \sqrt{5}-\sqrt{3})}$
View full solution →$\frac{1}{(2 \sqrt{5}-\sqrt{3})}$
Rationalise the denominator of the following:
$\frac{3-2 \sqrt{2}}{3+2 \sqrt{2}}$
View full solution →$\frac{3-2 \sqrt{2}}{3+2 \sqrt{2}}$
Rationalise the denominator of the following:
$\frac{\sqrt{3}-1}{\sqrt{3}+1}$
View full solution →$\frac{\sqrt{3}-1}{\sqrt{3}+1}$
Rationalise the denominator of the following:
$\frac{1}{(\sqrt{6}-\sqrt{3})}$
View full solution →$\frac{1}{(\sqrt{6}-\sqrt{3})}$
Separate the rationals and irrationals from among the following numbers:
(i) [-8, (ii ) $\sqrt{25}$, (iii) $\frac{-3}{5}$, (iv)$\frac{-3}{5}$, (v) 0, (vi) $\pi$, (vii) $\sqrt[3]{5}$, (viii) $2 . \overline{4}$, (ix) $-\sqrt{3}$]
View full solution →(i) [-8, (ii ) $\sqrt{25}$, (iii) $\frac{-3}{5}$, (iv)$\frac{-3}{5}$, (v) 0, (vi) $\pi$, (vii) $\sqrt[3]{5}$, (viii) $2 . \overline{4}$, (ix) $-\sqrt{3}$]
Ms Mehta teaches maths in a school. One day after teaching the lesson of number system, she wanted to check the understanding of the students of her class. So, she wrote two numbers, $\frac{3}{11}$ and $0 . \overline{52}$ on the blackboard and asked few questions based on them. You please try to answer the following questions asked by Ms Mehta.
Q.1. The decimal expansion of $\frac{3}{11}$ is:
(a) terminating
(b) non-terminating
(c) non-terminating non-repeating
(d) non-terminating repeating
Q.2. $0 . \overline{52}$ is:
(a) non-terminating non repeating
(b) non-terminating repeating
(c) non-terminating
(d) terminating
Q.3. The decimal form of $\frac{3}{11}$ is:
(a) 0.27 (b) 0.2727 (c) $0 . \overline{27}$ (d) 0.3
Q.4. $0 . \overline{52}$ as a vulgar fraction becomes:
(a) $\frac{52}{99}$ (b) $\frac{52}{100}$ (c) $\frac{26}{25}$ (d) $\frac{13}{25}$
Q.5. The sum of $0 . \overline{52}$ and $\frac{3}{11}$ is:
(a) $\frac{79}{99}$ (b) $\frac{70}{99}$ (c) $\frac{52}{99}$ (d) $\frac{40}{99}$
View full solution →Q.1. The decimal expansion of $\frac{3}{11}$ is:
(a) terminating
(b) non-terminating
(c) non-terminating non-repeating
(d) non-terminating repeating
Q.2. $0 . \overline{52}$ is:
(a) non-terminating non repeating
(b) non-terminating repeating
(c) non-terminating
(d) terminating
Q.3. The decimal form of $\frac{3}{11}$ is:
(a) 0.27 (b) 0.2727 (c) $0 . \overline{27}$ (d) 0.3
Q.4. $0 . \overline{52}$ as a vulgar fraction becomes:
(a) $\frac{52}{99}$ (b) $\frac{52}{100}$ (c) $\frac{26}{25}$ (d) $\frac{13}{25}$
Q.5. The sum of $0 . \overline{52}$ and $\frac{3}{11}$ is:
(a) $\frac{79}{99}$ (b) $\frac{70}{99}$ (c) $\frac{52}{99}$ (d) $\frac{40}{99}$
Case Study II: Ms Mehta teaches maths in a school. One day after teaching the lesson of number system, she wanted to check the understanding of the students of her class. So, she wrote two numbers, $\frac{3}{11}$ and $0 . \overline{52}$ on the blackboard and asked few questions based on them. You please try to answer the following questions asked by Ms Mehta.
1. The decimal expansion of $\frac{3}{11}$ is:
(a) terminating (b) non-terminating
(c) non-terminating non-repeating (d) non-terminating repeating
2. $0 . \overline{52}$ is:
(a) non-terminating non repeating (b) non-terminating repeating
(c) non-terminating (d) terminating
3. The decimal form of $\frac{3}{11}$ is:
(a) 0.27 (b) 0.2727 (c) $0 . \overline{27}$ (d) 0.3
4. $0 . \overline{52}$ as a vulgar fraction becomes:
(a) $\frac{52}{99}$ (b) $\frac{52}{100}$(c) $\frac{26}{25}$ (d) $\frac{13}{25}$
5. The sum of $0 . \overline{52}$ and $\frac{3}{11}$ is:
(a) $\frac{79}{99}$ (b) $\frac{70}{99}$ (c) $\frac{52}{99}$ (d) $\frac{40}{99}$
View full solution →1. The decimal expansion of $\frac{3}{11}$ is:
(a) terminating (b) non-terminating
(c) non-terminating non-repeating (d) non-terminating repeating
2. $0 . \overline{52}$ is:
(a) non-terminating non repeating (b) non-terminating repeating
(c) non-terminating (d) terminating
3. The decimal form of $\frac{3}{11}$ is:
(a) 0.27 (b) 0.2727 (c) $0 . \overline{27}$ (d) 0.3
4. $0 . \overline{52}$ as a vulgar fraction becomes:
(a) $\frac{52}{99}$ (b) $\frac{52}{100}$(c) $\frac{26}{25}$ (d) $\frac{13}{25}$
5. The sum of $0 . \overline{52}$ and $\frac{3}{11}$ is:
(a) $\frac{79}{99}$ (b) $\frac{70}{99}$ (c) $\frac{52}{99}$ (d) $\frac{40}{99}$
Case Study I: The union of the set of rational numbers (Q) and irrational numbers (P) form the set of real numbers (R). Rational numbers are the set of numbers which can be written in the form $\frac{a}{b}$ , where a and b are integers and $b \neq 0$. The decimal expansion of a rational number is either terminating or non-terminating repeating. The number which cannot be expressed in the form $\frac{a}{b}$ are called irrational numbers. The decimal expansion of irrational numbers is non-terminating non-repeating.
Based on the above information, answer the following questions:
1. Every rational number is:
(a) a natural number (b) a whole number
(c) an integer (d) a real number
2. Every real number is:
(a) an integer
(b) a rational number
(c) an irrational number
(d) either a rational number or an irrational number.
3. The sum of two irrationals is:
(a) irrational (b) rational
(c) either rational or irrational (d) neither rational nor irrational
4. The product of a rational and an irrational number is:
(a) an irrational number
(b) a rational number
(c) either a rational number or an irrational number
(d) neither a rational number nor an irrational number
5. The number of irrational numbers is:
(a) finite (b) infinite
(c) neither finite nor infinite (d) none of these
Classify the rational and irrational numbers from the following:
[(i)5, (ii)$\frac{9}{14}$, (iii)$\sqrt{3}$, (iv)$\pi$, (v)3.1416, (vi)$\sqrt{4}$, (vii)$-\sqrt{5}$, (viii)$\sqrt[3]{8}$,(ix) $\sqrt[3]{3}$, (x)$2 \sqrt{6}$, (xi)$0 . \overline{36}$,(xii) 0.202202220…, (xiii)$\frac{2}{\sqrt{3}}$, (xiv) $\frac{22}{7}$]
View full solution →[(i)5, (ii)$\frac{9}{14}$, (iii)$\sqrt{3}$, (iv)$\pi$, (v)3.1416, (vi)$\sqrt{4}$, (vii)$-\sqrt{5}$, (viii)$\sqrt[3]{8}$,(ix) $\sqrt[3]{3}$, (x)$2 \sqrt{6}$, (xi)$0 . \overline{36}$,(xii) 0.202202220…, (xiii)$\frac{2}{\sqrt{3}}$, (xiv) $\frac{22}{7}$]
The product of a rational and an irrational is a rational.
The sum of a rational and an irrational is an irrational.
The product of two irrationals is an irrational.
The product of two rationals is a rational.
The sum of two irrationals is an irrational.
When written in decimal form, which of the following will be a non-terminating and non-repeating number?
- A$1^{1 / 9}$
- ✓$2^{1 / 9}$
- C$2^{-9}$
- D$9^{1 / 2}$
Answer: B.
View full solution →$1 . \overline{9}-1.9$ is equal to :
- A0
- B1
- C0.09
- ✓0.1
Answer: D.
View full solution →$\sqrt[4]{\sqrt[3]{3^2}}$ can be expressed as :
- A$3^6$
- B$6^{1 / 3}$
- C$3^{1 / 12}$
- ✓$3^{1 / 6}$
Answer: D.
View full solution →$0.6+0 . \overline{7}+0.4 \overline{7}$ is equal to :
- A$\frac{155}{90}$
- B$\frac{147}{90}$
- ✓$\frac{167}{90}$
- Dnone of these
Answer: C.
View full solution →Four rational numbers $p, q, r$ and $s$ are such that $q$ is the reciprocal of $p$ and $s$ is the reciprocal of $r$. The value of the expression
$\left\{\left(p+\frac{1}{q}\right) \div\left(r+\frac{1}{s}\right)\right\} \quad\left\{\left(s+\frac{1}{r}\right) \quad\left(q+\frac{1}{p}\right)\right\}$ is equal to:
$\left\{\left(p+\frac{1}{q}\right) \div\left(r+\frac{1}{s}\right)\right\} \quad\left\{\left(s+\frac{1}{r}\right) \quad\left(q+\frac{1}{p}\right)\right\}$ is equal to:
- ✓1
- B0
- C$p r$
- D$\frac{s}{q}$
Answer: A.
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