Find the smallest number by which $\sqrt{27}$ should be multiplied so as to get a rational number.
Step-by-Step Solution
Key Concept: $\sqrt{27} = 3\sqrt{3}$. Multiplying by $\sqrt{3}$ gives $3 \times 3 = 9$ (rational).
$\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$. [1.0 Mark]
Smallest number to multiply by is $\sqrt{3}$ because $3\sqrt{3} \times \sqrt{3} = 9$ (rational). [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Simplifying $\sqrt{27} = 3\sqrt{3}$: 1.0 Mark
Identifying factor $\sqrt{3}$: 1.0 Mark
Correct Answer: