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Simplify and find the value of $2 5 − 3 − 3 3 + 2 − 2 5 − 2$ .

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53 + 23 + 723

53 − 23 + 723

53 − 23 − 723

53 + 23 − 723

answer is B.

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Detailed Solution

Given,

2 5 − 3 − 3 3 + 2 − 2 5 − 2

.
Simplify the given question,

2 5 − 3 − 3 3 + 2 − 2 5 − 2

By rationalizing the denominator, Apply formula,

a 2 − b 2 = (a − b) (a + b)

on the expression.

⇒ 2 5 − 3 × 5 + 3 5 + 3 − 3 3 + 2 × 3 − 2 3 − 2 − 2 5 − 2 × 5 + 2 5 + 2

⇒ 2 (5 + 3) 5 − 3 − 3 (3 − 2) 3 − 2 − 2 (5 + 2) 5 − 2

⇒ 2 (5 + 3) 2 − 3 (3 − 2) 1 − 2 (5 + 2) 3

⇒ 5 + 3 − 33 + 32 − 25 − 22 3

Simplifying further.

⇒ 5 + 3 (1 − 3) − 25 − 22 3 + 32

⇒ 5 − 23 − 25 − 22 3 + 32

⇒ 35 − 63 − 25 − 22 + 92 3

⇒ 53 − 23 + 723

Hence, the correct option is 2.

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