Using Euclid’s Algorithm, find the HCF of 2048 and 960.

Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.

Find three rational numbers lying between 0 and 0.1. Find twenty rational numbers between 0 and 0.1. Give a method to determine any number of rational numbers between 0 and 0.1.

Which of the following rational numbers have the terminating decimal representation?

(i) 3/5

(ii) 7/20

(iii) 2/13

(iv) 27/40

(v) 133/125

(vi) 23/7

Write the following rational numbers in decimal form:

(i) 42/100

(ii) 27/8

(iii) 1/5

(iv) 2/13

(v) 327/500

(vi) 5/6

(vii) 1/7

(viii) 11/17

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