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Simplify the expression by rationalizing the denominators.

$5 + 2 5 − 2 + 5 − 2 5 + 2$

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5223

5423

5623

5923

answer is B.

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Detailed Solution

Given ,

5 + 2 5 − 2 + 5 − 2 5 + 2

.
Solve the expression by rationalising the denominator,

= 5 + 2 5 − 2 × 5 + 2 5 + 2 + 5 − 2 5 + 2 × 5 − 2 5 − 2

= (5 + 2) 2 (25 − 2) + (5 − 2) 2 (25 − 2)

= (5 + 2) 2 23 + (5 − 2) 2 23

Simplify further,

= (5 + 2) 2 + (5 − 2) 2 23

= 25 + 2 + 102 + 25 + 2 − 102 23 = 5423

Hence, the correct option is 2.

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