Show that 3√2 is irrational

Solution:

We will use the contradiction method to show that 3√2 is an irrational number.

Let us assume that 3√2 is a rational number in the form of p/ q where p and q are coprimes and q ≠ 0.

3√2 = p/ q

Divide both sides by 3.

3√2 / 3 = p/q × 1/ 3.

√2 = p/ 3q

p/ 3q is a rational number.

Since we know that √2 is an irrational number. 

Thus, a rational number can not be equal to an irrational number

☛ Check: NCERT Solutions for Class 10 Maths Chapter 1

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Show that 3√2 is irrational

Summary: 

Hence proved that 3√2 is an irrational number using contradiction

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