Show that 5 - √3 is irrational

Solution: 

We will use the contradiction method to show that 5 - √3 is an irrational number.

Let us assume that 5 - √3 is a rational number in the form of p/ q where p and q are coprimes and q ≠ 0.

5 - √3 = p /q

Add √3 to both sides.

5 - √3 + √3 = p /q + √3

 5 = p/ q + √3

Subtract both sides p/ q.

5 - p/ q = √3

(5q - p)/ q = √3

Since we already know that √3 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 5 - √3 is irrational

Summary:

Hence proved that 5 - √3 is an irrational number using contradiction.

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