R. D. Sharma Solutions for Chapter: Real Numbers, Exercise 5: EXERCISE 1.5

Show that $7\sqrt{5}$ is irrational.

Show that the following number are irrational:

$6+\sqrt{2}$

Show that the following number are irrational:

$3-\sqrt{5}$

Prove that $\frac{2}{\sqrt{7}}$ is an irrational number.

Prove that following numbers are irrationals:

$\frac{3}{2\sqrt{5}}$

Prove the given number as an irrational:

$4+\sqrt{2}$

Prove the following number as an irrational:

$5\sqrt{2}$

Given that $\sqrt{2}$ is irrational, prove that $(5+3\sqrt{2})$ is an irrational number.