The decimal expansion of the number √2 is
a. a finite decimal
b. 1.41421
c. non-terminating recurring
d. non-terminating non-recurring

Solution:

We know that

√2 = 1.41421

A number which cannot be expressed in the form p/q where p and q are integers and q ≠ 0 is called an irrational number.

Here √2 is an irrational number

So the decimal expansion is non terminating and non recurring.

Therefore, the decimal expansion is non-terminating and non-recurring.

✦ Try This: Find a rational number between 7/6 and 5/6.

Rational numbers between 7/6 and 5/6 can be written as

(7/6 + 5/6)/2

Taking LCM

= [(7 + 5)/6]/2

By further calculation

= (12/6)/2

= 2 × 1/2

= 1

Therefore, the rational number is 1.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1

NCERT Exemplar Class 9 Maths Exercise 1.1 Problem 5

The decimal expansion of the number √2 is a. finite decimal, b. 1.41421, c. non-terminating recurring, d. non-terminating non-recurring

Summary:

The decimal expansion of the number √2 is non-terminating non-recurring. As √2 = 1.41421 the decimal expansion is non-terminating non-recurring

☛ Related Questions:

• Which of the following is irrational? a. √4/9, b. √12/√3, c. √7, d. √81
• Which of the following is irrational? a. 0.14, b. 0.14 bar, 16 c.0.bar 1416, d. 0.4014001400014…
• A rational number between √2 and √3 is a. (√2 + √3)/2, b. √2.√3/2, c. 1.5, d. 1.8