Prove that number `(log)_2 7` is an irrational number.

Define an irrational number.

Prove that sqrt(3)+\ sqrt(5) is an irrational number.

prove that sqrt(3)-sqrt(2) is an irrational number.

Prove that sqrt(3)+sqrt(4) is an irrational number.

Show that log_(4)18 is an irrational number.

Given that sqrt(5) is irrational, prove that 2sqrt(5)-3 is an irrational number.

Are the following pairs of statements negations of each other:(i) The number x is not a rational number. The number x is not an irrational number.(ii) The number x is a rational number. The number x is an irrational number.

Are the following pairs of statements negations of each other: (i) The number x is not a rational number. The number x is not an irrational number. (ii) The number x is a rational number. The number x is an irrational number.

Given that sqrt(2) is a irrational prove that (5+3sqrt(2)) is an irrational number

Give an example of each, of two irrational numbers whose: (i) difference is a rational number. (ii) difference is an irrational number. (iii) sum is a rational number. (iv) sum is an irrational number. (v) product is a rational number. (vi) product is an irrational number. (vii) quotient is a rational number. (viii) quotient is an irrational number.