Which of the following is irrational
a. √4/9
b. √12/√3
c. √7
d. √81

Solution:

Let us simplify each option

a. √4/9 = 2/3

b. √12/√13 = 2√3/ √3 = 2

c. √7 = 2.64575131106

d. √81 = 9

Here we know that √7 = 2.64575131106 is a non terminating decimal expansion

Therefore, √7 is irrational.

✦ Try This: Which of the following is irrational? a. √9/16, b. √27/√3, c. √6, d. √64

Let us simplify each option

a. √9/16 = 3/4

b. √27/√13 = 3√3/ √3 = 3

c. √6 = 2.4494897427831

d. √64 = 8

Here we know that √6 = 2.4494897427831 is a non terminating decimal expansion

Therefore, √6 is irrational.

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

NCERT Exemplar Class 9 Maths Exercise 1.1 Problem 6

Which of the following is irrational? a. √4/9, b. √12/√3, c. √7, d. √81

Summary:

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. √7 is irrational

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