Class 10 Irrational Numbers — practice questions with answers

Number Systems · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Which of the following numbers is irrational?

A $2$
B0.75
C $\frac{3}{7}$
D $\frac{16}{4}$

Show answer

Answer: A)

2

2

is non-terminating non-recurring, so it is irrational. 0.75 =

\frac{3}{4}

\frac{3}{7}

and

\frac{16}{4}

= 4 are all rational.

2. On rationalising the denominator of

\frac{1}{2}

, we get:

A $\frac{2}{2}$
B $\frac{2}{2}$
C $\frac{1}{2}$
D $2$

Show answer

Answer: A)

\frac{2}{2}

\frac{1}{2} \times \frac{2}{2}

\frac{2}{2}

3. Riya marks a square tile of side 1 metre on the floor. She measures its diagonal using the Pythagoras rule.
The diagonal length (in metres) is:

A $2$ , an irrational number
B2, a rational number
C1.5, a rational number
D $3$ , an irrational number

Show answer

Answer: A)

2

, an irrational number

Diagonal =

1^{2} + 1^{2}

2

, which is irrational.

4. Vikram constructs

2

on a number line by drawing a right triangle with both legs 1 unit, then swinging the hypotenuse onto the line with a compass.
How long is the hypotenuse he marks?

A $2$ units
B2 units
C1 unit
D $3$ units

Show answer

Answer: A)

2

units

With legs 1 and 1, the hypotenuse =

1^{2} + 1^{2}

2

units, which is then marked on the number line.

5. Two students simplify

\frac{3 + 1}{3 - 1}

by rationalising.
The correct simplified value is:

A $2 + 3$
B $2 - 3$
C $1 + 3$
D $4 + 3$

Show answer

Answer: A)

2 + 3

Multiply numerator and denominator by

(3 + 1)

: numerator =

(3 + 1)^{2}

4 + 23

; denominator = 3 - 1 = 2. So value =

\frac{4 + 2 3}{2}

2 + 3

Practise all 50 questions free →

10 free questions a day without an account — unlimited with a free account.