Question

√P + √Q is …...… where P and Q are natural numbers.

A) real number

B) irrational number 

C) natural number 

D) rational number

Answer 1

Correct option is (A) real number

(i) If P = 1, Q = 4

Then \(\sqrt P+\sqrt Q=\sqrt1+\sqrt4\) = 1+2 = 3 which is a rational number.

(ii) If P = 1, Q = 2

Then \(\sqrt P+\sqrt Q=\sqrt1+\sqrt2\) \(=1+\sqrt2\) which is an irrational number.

Thus, \(\sqrt P+\sqrt Q\) is rational or irrational. It is depends on fixed value of P and Q. But if P and Q are natural numbers (or positive rational numbers) then \(\sqrt P+\sqrt Q\) always a real number.

Answer 2

Correct option is A) real number