{{5}-{3}}{{5}+{3}} = ?

Correct Answer is : 4−154-{15}4−15

Correct Answer is : 4−154-{15}4−15

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IBPS Clerk Prelims Model Paper 3

Question : 10 of 100

Marks: +1, -0

\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}

= ?

Solution:

Concept:

To simplify a surd fraction, multiply the numerator and denominator by the conjugate of the denominator.

Explanation:

Given expression

= \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}

Multiply numerator and denominator by the conjugate

\sqrt{5}-\sqrt{3}

= \frac{(\sqrt{5}-\sqrt{3})^2}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}

Use

(a-b)^2=a^2+b^2-2ab

and

(a+b)(a-b)=a^2-b^2

= \frac{5+3-2\sqrt{15}}{5-3}

= \frac{8-2\sqrt{15}}{2}

= \frac{2(4-\sqrt{15})}{2}

= 4-\sqrt{15}

Answer:

4-\sqrt{15}

, which is option B.

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