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CBSE · Class 9 · Mathematics

The World of Numbers

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
Which of these is irrational?
  1. √20
  2. √49
  3. 2/4
  4. 0.87
2.
The decimal expansion of 4/15 is:
  1. terminating
  2. cannot be found
  3. non-terminating non-repeating
  4. non-terminating repeating
3.
(√11 + √23)(√11 − √23) equals:
  1. 12
  2. √253
  3. 34
  4. −12
4.
(8 + √10)2 equals:
  1. 74 + 16√10
  2. 74 + 8√10
  3. 164 + 16√10
  4. 74
5.
Which of these is irrational?
  1. π
  2. 0.5
  3. 22/7
  4. 3.14
6.
1/√14 with a rational denominator is:
  1. 1/14
  2. 14/√14
  3. √14
  4. √14/14
7.
The value of 8 raised to the power 1/3 is:
  1. 3
  2. 2
  3. 4
  4. 8
8.
Assertion (A): √48 is an irrational number.
Reason (R): The square root of a positive integer that is not a perfect square is irrational.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
Rationalise the denominator: 1/(6 + √10)
10.
Simplify: 4√5 + 4√20
11.
Write 0.616161… (61 repeating) in the form p/q.
12.
Simplify: √20 × √19
13.
Simplify: 9 to the power 2/3 × 9 to the power 1/3
14.
Find the value of 125 raised to the power −1/3.
15.
Write 73/80 in decimal form.
16.
Rationalise the denominator: √13/√14
Section C — Word problems4 × 4 = 16 marks
17.
A square plot has an area of 200 m2. Find the length of its side in simplest surd form.
18.
A rectangle is (5 + √5) cm long and (5 − √5) cm wide. Find its area.
19.
The two shorter sides of a right-angled triangle are √3 cm and √28 cm. Find the longest side.
20.
A wire 21√13 m long is cut into 3 equal pieces. How long is each piece?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 9 · Mathematics

Answer key

The World of Numbers · AW-9M-NUM-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(a) √2020 is not a perfect square
2(d) non-terminating repeatingthe denominator 15 has a prime factor other than 2 and 5
3(d) −12(√11)2 − (√23)2 = 11 − 23
4(a) 74 + 16√1082 + 2 × 8 × √10 + 10 = 74 + 16√10
5(a) π22/7 and 3.14 are only approximations of π
6(d) √14/14multiply top and bottom by √14
7(b) 28 = 23, so (23) to the 1/3 = 21 = 2
8(a) Both A and R are true, and R is the correct explanation of A.A is true: 48 is not a perfect square. R is true and explains A.
9(6 − √10)/26multiply by (6 − √10); denominator 62 − 10 = 26
1012√5√20 = 2√5, so 4√5 + 8√5 = 12√5
1161/99x = 0.6161…, 100x − x = 61, x = 61/99 = 61/99
122√95√380 = 2√95
139add the powers: 2/3 + 1/3 = 1; 91 = 9
141/5125 = 53; power −1/3 gives 5−1 = 1/5
150.912580 has only 2 and 5 as prime factors, so it terminates: 73 ÷ 80 = 0.9125
16√182/14multiply by √14: √182/14 = √182/14
1710√2 mside = √200 = √(100 × 2) = 10√2
1820 cm2(5 + √5)(5 − √5) = 52 − 5 = 20
19√31 cm√(3 + 28) = √31 = √31
207√13 m21√13 ÷ 3 = 7√13