# Class 10 real numbers extra questions

Given below are the important and extra questions for Chapter 1 class 10 maths real numbers
a. Long answer questions
b. True and false questions
c. Multiple choice questions(MCQ)
d. Short Answer type
e. Irrational number proof questions
f. Cross-word Puzzle

## Long answer questions

Question 1
Without actually performing division, state which of these number will terminating decimal expression or non terminating repeating decimal expression
1. $\frac {7}{25}$
2. $\frac {3}{7}$
3. $\frac {29}{343}$
4. $\frac {6}{15}$
5. $\frac {77}{210}$
6. $\frac {11}{67}$
7. $\frac {15}{27}$
8. $\frac {11}{6}$
9. $\frac {343445}{140}$

Question 2
Using Euclid’s theorem to find the HCF between the following numbers
a. 867 and 225
b. 616 and 32

Question 3
Write 10 rational number between
a. 4 and 5
b. 1/2 and 1/3
Question 4
Represent in rational form.
a. 1.232323….
b. 1.25
c. 3.67777777
Question 5
a. Prove that 2+√3 is a irrational number
b. Prove that 3√3 a irrational number

## True or False statement

Question 6
Mark T/F as appropiate:
a. Number of the form $2n +1$ where n is any positive integer are always odd number
b. Product of two prime number is always equal to their LCM
c. $\sqrt {3} \times \sqrt {12}$ is a irrational number
d. Every integer is a rational number
e. The HCF of two prime number is always 1
f. There are infinite integers between two integers
g. There are finite rational number between 2 and 3
h. √3 Can be expressed in the form √3/1,so it is a rational number
i. The number 6n for n in natural number can end in digit zero
j. Any positive odd integer is of the form 6m+1 or 6m+3 or 6m +5 where q is some integer

## Multiple choice Questions

Question 7
the HCF (a, b) =2 and LCM (a, b) =27. What is the value $a \times b$
a. 25
b. 9
c. 27
d. 54

Question 8
2+√2 is a
a. Non terminating repeating
b. Terminating
c. Non terminating non repeating
d. None of these

Question 9
if a and b are co primes which of these is true
a. LCM (a, b) =aXb
b. HCF (a, b)= aXb
c. a=br
d. None of these

Question 10
A rational number can be expressed as terminating decimal when the factors of the denominator are
a. 2 or 5 only
b. 2 or 3 only
c. 3 or 5 only
d. 3 or 7 only

Question 11
if $x^2 =3 \;, \; y^2=9 \; ,\; z^3=27$, which of these is true
a. x is a irrational number
b. y is a rational number
c. z is rational number
d.All of the above

## Short answer question

Question 12
Find the HCF and LCM of these by factorization technique
a.27,81
b. 120 ,144
c. 29029 ,580

Question 13
Find all the positive integral values of p for which  $p^2 +16$ is a perfect square?

Question 14
Find the nature of the product $(\sqrt {2} - \sqrt {3}) ( \sqrt {3} + \sqrt {2})$ ?

Question 15
Show that 4n can never end with the digit zero for any natural number n.

Question 16
Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

## Irrational number proof questions

Question 17
Show that $3 + 5 \sqrt {2}$ is an irrational number. Is sum of two irrational numbers always an irrational number?

Question 18
Prove that $\sqrt {3}$ is an irrational number and hence show that $2\sqrt {3}$ is also an irrational number.

Question 19
Prove that $5 - \sqrt {3}$ is an irrational number.

Question 20
Prove that $2 \sqrt {5}$ is an irrational number.
Question 21
Show that $(\sqrt {3} + \sqrt {5})^2$ is an irrational number.

Question 22
Prove that $4 - \sqrt {5}$ is an irrational number.
Question 23
Prove that $\sqrt {5}$ is an irrational number.

Question 24
Prove that  √2 + 1/√2 is an irrational number
Question 25
Prove that for any positive integer n, n3 – n is divisible by 6.

Question 26
If n is rational and √m   is irrational, then prove that (n + √m) is irrational.
Question 27
Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer

Question 28
Prove that √11 is irrational.
Question 29
Show that 3√2 is irrational.
Question 30
Prove that the sum of a rational number and an irrational number is always irrational.

Question 31
The product of a non-zero rational and an irrational number is
(A) always irrational
(B) always rational
(C) rational or irrational
(D) one

Question 32
Prove that √p + √q is irrational, where p, q are primes.
Question 33
Prove that one of any three consecutive positive integers must be divisible by 3.

## Cross-word Puzzle to check your Real number knowledge

Across
2. Number which are not divisible by any other number except 1
6. decimal expression can be expressed in the form 1/2m5n
Down
1. Number which can be written as product of prime
3. In Euclid division lemma a=bq + r , it is the value r
4. HCF can be found using this division algorithm
5. In Euclid division lemma a=bq + r , it is the value b
7. Numbers of the forms p/q

## Summary

This class 10 real numbers extra questions with answers is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.

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### Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20