Rational and Irrational Numbers Class 9 OP Malhotra Ch-Test ICSE Maths Solutions 2026 Ch-1. We Provide Step by Step Solutions / Answer of Rational and Irrational Numbers OP Malhotra Maths . Visit official Website CISCE for detail information about ICSE Board Class-9 Mathematics.
Rational and Irrational Numbers Class 9 OP Malhotra Exe-1A ICSE Maths Solutions Ch-1
| Board | ICSE |
| Publications | S Chand |
| Subject | Maths |
| Class | 9th |
| Chapter-1 | Rational and Irrational Numbers |
| Writer | OP Malhotra |
| Ch-Test | Extra Practice Questions |
| Edition | 2025-2026 |
Ch-Test on Rational and Irrational Numbers
Numbers Class 9 OP Malhotra ICSE Maths Solutions Ch-1
Que-1: A number is an irrational number if and only if its decimal representation is
(a) non-terminating
(b) non-terminating and repeating
(c) non-terminating and non-repeating
(d) terminating
Sol: (c) non-terminating and non-repeating
Que-2: Which of the following is an irrational number?
(a) √29
(b) √441
(c) 0.5948
(d) 5.(318)¯¯
Sol: (a) √29
29−−√ is irrational number as 29 is not a perfect square.
Que-3: (- 2 – √3) (- 2 + √3) when simplified is
(a) positive and irrational
(b) positive and rational
(c) negative and irrational
(d) negative and rational
Sol: (b) positive and rational
(- 2 – √3) (- 2 + √3) = (- 2)² – (√3)²
= 4 – 3 = 1
Which is positive and rational.
Que-4: If √6 x √15 = x√10 , then the value of x is
(a) 3
(b) ± 3
(c) √3
(d) √6
Sol: (a) 3
√6 x √15 = x√10
⇒ √6×15 = x√10
⇒ √90 = x√10
⇒ √9×10 = x√10
⇒ 3√10 = x√10
Comparing, we get
∴ x = 3
Que-5: Two rational numbers between 27 and 214 are
(a) 114 and 214
(b) 12 and 32
(c) 314 and 37
(d) 514 and 814
Sol: (d) 514 and 814
Two rational numbers between 27 and 214 are
514 and 814
∵ 27 and 57 = 414 and 1014
and 5 and 8 lie between 4 and 10
Que-6: An irrational number between 57 and 79 is
(a) 0.75
(b) √6
(c) 0.7507500075000…
(d) 0.7512
Sol: (c) 0.7507500075000…
An irrational number between 57 and 79 either √6 or 0.7507500075000…
∵ 0.75 and 0.7512 are rational number
Now √6
Which does not line between 57 and 79
∴ 0.7507500075000… is irrational number between 57 and 79
Question 7. If √2 = 1.4142, then the value of 7/(3+√2) correct to two decimal places is
(a) 1.59
(b) 1.60
(c) 2.58
(d) 2.57
Sol: (a) 1.59
√2 = 1.4142
7(3+√2) = {7×(3-√2)} / [(3+√2)(3−√2)]
(Rationalising denominator)
{7(3−√2)}/(9−2) = {7(3−√2)}/7
= 3 – √2
= 3 – 1.4142 = 1.5858 = 1.59
Que-8: Taking √3 as 1.732 and √2 = 1.414, the value of 1/(√3+√2) is
(a) 0.064
(b) 0.308
(c) 0.318
(d) 2.146
Sol: (c) 0.318
√3 = 1.732, √2 = 1.414
1/(√3+√2) = (√3−√2) / {(√3+√2)(√3−√2)}
(Rationalising denominator)
(√3−√2)/(3−2) = (√3−√2)/1
=√3 − √2
= 1.732 – 1.414 = 0.318
Question 9. If x = √3 + √2, then the value of x + (1/x) is
(a) 2
(b) 3
(c) 2√2
(d) 2√3
Sol: (d) 2√3
x = √3 + √2
1/x = 1/(√3+√2) = (√3−√2) / {(√3+√2)(√3−√2)}
(Rationalising denominator)
= (√3−√2)/(3−2) = (√3−√2)/1
= √3 − √2
x + (1/x) = √3 + √2 + √3 − √2
= 2√3
Que-10: If x = 2 + √3, then the value of √x + 1/√x is
(a) 3 + √3
(b) √6
(c) 2√6
(d) 6
Sol: (b) √6
x = 2 + √3
1/x = 1/(2+√3) = {1(2−√3)} / {(2+√3)(2−√3)}
(Rationalising denominator)
(2−√3)/{(2)²−(√3)²} = (2−√3)/(4−3) = 2 − √3
∴ x + (1/x) = 2 + √3 + 2 – √3 = 4
and (√x + 1/√x)² = x + (1/x) + 2
= 4 + 2 = 6
√x + (1/√x) = ±√6 = √6
— : End of Rational and Irrational Numbers Class 9 OP Malhotra Ch-Test ICSE Maths Step by step Solutions :–
Return to :– OP Malhotra S Chand Solutions for ICSE Class-9 Maths
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