Question

Rationalise the denominator
• 4/√2+√3
• 2/√2-√5​

Answer 1

Answer:

1) 4/√2+√3.

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

Multiply numerator & denominator by √2-√3.

4/√2+√3×√2-√3/√2-√3.

4(√2-√3)/(√2)²-(√3)². (Because (a+b)×(a-b)=a²-b² where a=√2 & b=√3).

4√2-4√3/2-3. (Because √ & ² will cancel).

4√2-4√3/-1. (Because +×-=- & largest number is important.

-4√2-4√3. (Because +÷-=-).

2) 2/√2-√5.

Rationalising denominator of √2-√5 is √2+√5.

Multiply numerator & denominator by √2+√5.

2/√2-√5×√2+√5/√2+√5.

2(√2+√5)/(√2)²-(√5)². (Because (a+b)×(a-b)=a²-b² where a=√2 & b=√5).

2√2+2√5/2-5. (Because √ & ² will cancel).

2√2+2√5/-3. (Because +×-=- & largest number is important.

-2√2+2√5/3. (Because +÷-=-).

I think this is your answer.