Question

give example of two distinct irrational number such that their a) sum id irrational b) difference is irrational c) product is irrational d) quotient is irrational​

Answer 1

1) Sum is irrational

Let (6+√7) and (-6+2√7) be two irrational numbers.

Sum=(6+√7)+(-6+2√7)

=3√7 which is an irrational number.

2) Difference is irrational

Let 3+4√5 and 3-√5 be two irrational numbers.

Difference=(3+4√5)-(3-√5)

=5√5 which is an irrational number.

3) Product is irrational

Let √2 and √3 be two irrational numbers.

Product=√2*√3

=√6 which is an irrational number.

4) Quotient is irrational

Let √10-√5 and √2-1 be two irrational numbers.

Quotient=√10-√5/√2-1

=√5(√2-1)/(√2-1)

=√5 which is an irrational number.

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