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Real Numbers
NCERT Exemplar Ch 01
CBSE_NCERT_EXEMPLAR_CH01
Grade 10

Question:

Which of the following is an irrational number?

$\sqrt{4}$
$\sqrt{9/16}$
$\sqrt{7}$
$0.375$

Step-by-Step Solution

Key Concept: Square root of a non-square prime number is always irrational.
Stepwise Solution:

$\sqrt{4}=2$ (rational), $\sqrt{9/16}=3/4$ (rational), $0.375=3/8$ (rational). [0.5 Mark]

$\sqrt{7}$ cannot be written as $p/q$ where $p, q \in \mathbb{Z}$, hence it is irrational. [0.5 Mark]

Marking Scheme:

• Correct evaluation of rational options: 0.5 Mark
• Correct selection: 0.5 Mark

Correct Answer: $\sqrt{7}$
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