(2√3+4√2)+( √3−2√2)=____.

Correct! Wrong!

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(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

√ (2025) is an irrational number.

Correct! Wrong!

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

28 ÷ 23 = ________.

Correct! Wrong!

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

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 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.

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.

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

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 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 value of 5 16×52 is ____.

Correct! Wrong!

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

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.

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 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.

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.

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.

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

Correct! Wrong!

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

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.

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.

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

Correct! Wrong!

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

CBSE Class 9th Maths - Irrational Numbers MCQs
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