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IBPS Clerk Prelims Model Paper 10

Question : 9 of 100

Marks: +1, -0

\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}

= ?

Solution:

Concept:

Simplify each square root by taking out perfect-square factors, then cancel the common term.

Explanation:

Write the numerator and denominator in factorised form.

\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}} = \frac{\sqrt{16 \times 2}+\sqrt{16 \times 3}}{\sqrt{4 \times 2}+\sqrt{4 \times 3}}

Take the perfect squares outside the roots.

= \frac{4\sqrt{2}+4\sqrt{3}}{2\sqrt{2}+2\sqrt{3}}

Factor out the common terms in the numerator and denominator.

= \frac{4(\sqrt{2}+\sqrt{3})}{2(\sqrt{2}+\sqrt{3})}

Cancel

(\sqrt{2}+\sqrt{3})

from numerator and denominator.

= \frac{4}{2} = 2

Answer:

The value is

2

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