√P + √Q is ……… where P and Q are natural numbers.
A) real number
B) irrational number
C) natural number
D) rational number
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√P + √Q is ……… where P and Q are natural numbers.
A) real number
B) irrational number
C) natural number
D) rational number
√P + √Q is ……… where P and Q are natural numbers.
A) real number
B) irrational number
C) natural number
D) rational number
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.
Correct option is A) real number