Rationalise the equation square root of 3-1/ square root of 3+1

Answer:

Given (√3 – 1)/(√3 + 1)

To rationalize the given equation we will multiply and divide the denominator by (√3 – 1)

⇒ (√3 – 1)(√3 – 1)/(√3 + 1)(√3 – 1)…………………….(1)

Denominator can be simplified using the formula (a– b2) = (a – b)(a + b)

Equation (1) becomes

⇒ (√3 – 1)2/(√3)2– (1)2………………………………….(2)

As we know (a – b)2 = a+ b2 – 2ab

(√3 – 1)= 3 + 1 – 2(√3)(1)

⇒ (√3 – 1)= 4 – 2 √3…………………………..(3)

As we know (a2 – b2) = (a + b)(a – b)

(√3)2– (1)= 3 – 1

(√3)2– (1)2  = 2………………………………..(4)

Substituting equation (3) and (4)  in equation (2) we get

⇒ (4 – 2 √3)/2

⇒ 2(2 – √3)/2

 (2 – √3)

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