Question

Rationalise the denominator of (i) 2/√3−1 (ii) 2+√3/ 2− √3

Answer 1

Answer:

(i) 2/√3-1.

Rationalising of denominator √3-1 is √3+1.

Multiply numerator & denominator by √3+1.

2/√3-1×√3+1/√3+1.

2√3-1/(√3)²-(1)². (Because a-b×a+b=a²-b² where a=√3 & b=1).

2√3-1/3-1.

2√3-1/2.

(ii) 2+√3/2-√3.

Rationalising of denominator 2-√3 is 2+√3.

Multiply numerator & denominator by 2+√3.

2+√3/2-√3×2+√3/2+√3.

(2)²+(√3)²/(2)²-(√3)². (Because a-b×a+b=a²-b² where a=2 & b=√3).

2+3/2-3. (Because +×-=- & largest number is important).

5/-1.

-5. (Because +÷-=-).

I think this is your answer.