Question

Rationalize the denominator of the following:

(i) 1/(√7 + 2) (ii) 5/(√3 + √2)
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Answer 1

Answer:

(i) 1/(√7+2).

Rationalising Denominator of (√7+2) is √7-2.

Multiply Numerator & Denominator by √7-2.

1/(√7+2)×√7-2/√7-2.

1(√7-2)/(√7)²-(2)². (Because a+b×a-b=a²-b² where a=√7 & b=2).

√7-2/7-2.

√7-2/5.

(ii) 5/(√3+√2).

Rationalising Denominator of (√3+√2) is √3-√2.

Multiply Numerator & Denominator by √3-√2.

5/√3+√2×√3-√2/√3-√2.

5√3-√2/(√3)²-(√2)². (Because a+b×a-b=a²-b² where a=√3 & b=√2).

5√3-√2/3-2.

5√3-√2/1.

5√3-√2.

I think this is your answer.