Question

Write the reciprocal of 5 +√2.

Answer 1

Answer:

1/5+√2 is the reciprocal..

1/5+√2*5-√2/5-√2 (conjugate)

5-√2/25-2

5-√2/23 .

Answer 2

Given :  5 +√2

The reciprocal of 5 +√2 is 1/5 +√2

To make the denominators free from square roots, we multiply the numerator and denominator by an irrational number. Such a number is called rationalisation factor. The rationalisation factor for 1/(a ± √b) is a -+ √b :  

The rationalisation factor for 5 +√2 is 5 - √2 :  

1/(5 +√2) = [1 × (5 -√2)] / [(5 +√2) × (5 -√2)]

We know that , (a + b)(a – b) = a² - b² :  

= (5 - √2)/ [5² - √2²]

=  (5 - √2)/ [25 - 2]

=  (5 - √2)/ 23

Hence , the reciprocal of 5 + √2 is 1/5 - √2 = 5 + √2.

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