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Rationalize the denominator of $3 − 22 3 + 22$ , and choose the option which indicates the rationalized form correctly.

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17 − 122

(3 − 22) 2

17 + 122

(3 + 22) 2

answer is A.

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Detailed Solution

We are given a fraction

3 − 22 3 + 22

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

(3 − 22)

, and simplify using the identity

a + b a − b = a 2 − b 2

Now use the identity

(a − b) 2 = a 2 − 2 a b + b 2

, and expand the above expression as follows,

(3 − 22) 2 = (3) 2 − 2 (3) (2 2) + (22) 2 = 9 − 122 + 8 = 17 − 122

So, the expression obtained after rationalizing the denominator of

3 − 22 3 + 22

17 − 122

.
Hence, the correct option is (1).

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