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Which of the following numbers is rational?
Question

Which of the following numbers is rational?

A.

23\frac{2}{√3}​​

B.

34\frac{√3}{4}​​

C.

(2549)\sqrt{(\frac{25}{49})}​​

D.

7√2

Correct option is C

Concept Used:

- A rational number is a number that can be expressed as a ratio of two integers (p/q) where q ≠ 0.
(ab)=ab \sqrt{(\frac{a}{b})} =\frac{ √a }{ √b}​​
- √(perfect square) = integer
Solution:
Option A: 2/√3 is irrational because √3 is irrational, and dividing by an irrational number results in an irrational number.

Option B: √3/4 is also irrational because √3 is irrational.

Option C: √(25/49) = √25 / √49 = 5/7 → This is a rational number because both 5 and 7 are integers.

Option D: 7√2 is irrational because √2 is irrational and multiplying an irrational number by a rational number (7) gives an irrational result.

Hence, the correct answer is: √(25/49)

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