Rationalize $53 − 42 43 + 32$ and choose the option which represents the rationalized form correctly.

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84 − 316 30

81 − 316 30

81 + 307 30

81 + 307 20

answer is A.

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Detailed Solution

We are given a fraction

53 − 42 43 + 32

which is to be rationalized.
To rationalize the fraction, we multiply both the numerator and the denominator by

43 + 32

and simplify using the identity

a + b a − b = a 2 − b 2

53 − 42 43 + 32

53 − 42 43 + 32 × 43 − 32 43 − 32

= 53 43 − 32 − 42 43 − 32 432 − 322 = 20 × 3 − 156 − 166 + 12 × 2 48 − 18 = 60 + 24 − 316 30 = 84 − 316 30

So, rationalizing the denominator of

53 − 42 43 + 32

, the result is obtained as

84 − 316 30

.
Hence, the correct option is (1).

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