√ (2025) is an irrational number.

Correct! Wrong!

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√2025=√(25×81)
= 5 × 9
= 45, which is a rational number.
Hence, √2025 is a rational number.

(5+2√3)(5−3√3)=____.

Correct! Wrong!

(5+2√3)(5−3√3)=5×5−5×3√3+√3×5−2√3×3√3
=25−15√3+10√3−18
=7−5√3
∴(5+2√3)(5−3√3)=7−5√3

The product of 3 and √5 is a rational number.

Correct! Wrong!

The product of a rational number and an irrational number is irrational as long as the rational is not zero.
3×√5=3√5,which is an irrational.
Hence, the product of 3 and √5 is an irrational number.

The number 3−√3 is a rational number.

Correct! Wrong!

The difference of a rational number and an irrational number is an irrational number.
Hence, the number 3−√3 is an irrational number.

A non-terminating and non-recurring decimal is known as an irrational number.

Correct! Wrong!

A non-terminating and non-recurring decimal is known as an irrational number.

If √5 = 2.236, then the value of 2/√5 up to three places of decimals is____.

Correct! Wrong!

2/√5 = 2/√5 X √5/√5
= 2/√5/5
= 2 X 2.236/5 (Given √5 = 2.236)
= 4.472/5
= 0.8944 Hence, the required three decimals value is 0.8944.

32 x 33 =_______.

Correct! Wrong!

32 x 33 = 32+3 ( am x an =am+n)
= 35
= 243
32 x 33= 243

The sum of a rational number and an irrational number is an irrational number.

Correct! Wrong!

Let us check this with an example:
Consider an irrational number √2= 1.41421...
The sum of 2 and √2 is again a non-terminating and non-recurring decimal number.
Hence, the sum of a rational number and an irrational number is an irrational number.

The value of 5 16×52 is ____.

Correct! Wrong!

516×52=5(16×2)
=532
= 525
= 2
Hence, the value of 516×52 is 2.

The number (2− √2)(2+ √2) is an irrational number.

Correct! Wrong!

(2−√2)(2+√2)=22−(2)2
= 4 − 2
= 2
Hence, the number (2−√2)(2+√2) is a rational number.

A number of the form p/q is called a rational number.

Correct! Wrong!

A number of the form p/q is called a rational number.

If 2n-1 + 2 n+1 = 320, then n =_______

Correct! Wrong!

Given, 2n-1 + 2n+1 = 320
2n-1 (1 + 22 )= 320
5 x 2n-1 =320
2n-1 = 320/5
2n-1 = 64
2n-1 = 26
n-1 = 6
n= 7 Given, 2n-1 + 2n+1 = 320
2n-1 (1 + 22 )= 320
5 x 2n-1 =320
2n-1 = 320/5
2n-1 = 64
2n-1 = 26
n-1 = 6
n= 7

Every whole number is a natural number.

Correct! Wrong!

'0' is a whole number but not a natural number.
Hence, every whole number except 0 is a natural number.

The product of two irrational numbers is always irrational.

Correct! Wrong!

Consider, √2×√8=√16
= 4
Hence, the product of two irrational numbers need not be an irrational number.

The number of rational numbers between two natural numbers is infinite.

Correct! Wrong!

The number of rational numbers between two natural numbers is infinite.

The square root of a positive integer is an irrational number.

Correct! Wrong!

Consider √9=3
Hence, the square root of a positive integer need not be an irrational number.

The solutions of the equation x2−9=0 are irrational numbers.

Correct! Wrong!

Given equation is x2−9=0.
⇒ x2=9
⇒x=√9
⇒x=±3
3 and −3 are rational numbers.
Hence, the solutions of x2−9=0 are rational numbers.

Which of the following is a rational number?

Correct! Wrong!

0.3333333... is a non-terminating and recurring decimal.
We know that,
a non-terminating and recurring decimal can be converted to the form of p/q, where p, q are integers and q ≠ 0.
0.3333333...=1/3
Hence, 0.3333333... is a rational number.

The value of π is approximately equal to 22/7.

Correct! Wrong!

The value of π is approximately equal to 22/7.

28 ÷ 23 = ________.

Correct! Wrong!

28 ÷ 23 = 28 / 23
= 28-3 ( am /an =am-n )
= 25
=32
28÷23 =32

(2√3+4√2)+( √3−2√2)=____.

Correct! Wrong!

(2√3+4√2)+( √3−2√2)=2√3+√3+4√2−2√2
=3√3+2√2
∴(2√3+4√2)+( √3−2√2)=3√3+2√2

CBSE Class 9th Maths - Irrational Numbers MCQs
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