Solve irrational number

Give an irrational numbers between 0.505005000 . . . and 0.525225222 . . . .

Which one of the following statement is true? (i) The sum of two irrational numbers is always an irrational number. (ii) The sum of two irrational numbers is always a rational number. (iii) The sum of two irrational numbers may be a rational number or irrational number. (iv) The sum of two irrational numbers is always an integer.

Which of the following is a correct statement? (A)Sum of two irrational numbers is always irrational (B) Sum of a rational and irrational number is always an irrational number (C)Square of an irrational number is always an irrational number (D) Sum of two rational numbers can never be an integer

Write a pair of irrational numbers whose sum is irrational .

Write a pair of irrational numbers whose product is irrational.

Write of pair of irrational numbers whose difference is irrational .

State true or false: (i) Negative of an irrational number is irrational . (ii) The product of a non- zero rational number and an irrational number is a rational number.

Define an irrational number.

Show that 5+2 sqrt(7) is an irrational number, where sqrt(7) is given to be an irrational number.

Show that 5+2 sqrt(7) is an irrational number, where sqrt(7) is given to be an irrational number.