If a is a positive rational number and n is a positive integer greater than 1, prove that an is a rational number.

Show that 3√6 and 3√3 are not rational numbers.

Show that 2 + √2 is not a rational number.

Give an example to show that the product of a rational number and an irrational number may be a rational number

Prove that √3 – √2 and √3 + √5 are irrational.

Express 7/64, 12/125 and 451/13 in decimal form

Mention whether the following numbers are rational or irrational:

(i) (√2 + 2)

(ii) (2 – √2) x (2 + √2)

(iii) (√2 + √3)2

(iv) 6/3√2

Given that √2 is irrational, prove that (5 + 3√2) is an irrational number.

Given that √2 is irrational, prove that (5 + 3√2) is an irrational number.

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