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Q.

If $2 = 1.4142,$ then what will be the value of the expression $2 − 1 2 + 1$ ?

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a

2.4142

b

5.8282

c

0.4142

d

0.1718

answer is C.

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Detailed Solution

The given expression is,

2 − 1 2 + 1

We could calculate the value of the above expression by rationalizing.
Therefore, multiply and divide the given expression by

2 − 1,

and we get,
Question Image

Question Image

⇒ 2 − 1 2 + 1 = 2 − 1 2 2 − 1 ⇒ 2 − 1 2 + 1 = 2 − 1

⇒ 2 − 1 2 + 1 = 1.4142... − 1 Given, 2 = 1.4142 ⇒ 2 − 1 2 + 1 = 0.4142

Therefore, the value of the expression

2 − 1 2 + 1 = 0.4142.

Hence, option (3) is correct.

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If 2 =1.4142, then what will be the value of the expression 2 − 1 2 + 1 ?