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Rationalise the denominator of: (√3 - √2)/(√3+√2) = ?​

Sagot :

SalmonWorldTopper

Step-by-step explanation:

Given :-

(√3-√2)/(√3+√2)

To find :-

Rationalised form = ?

Solution:-

Given that

(√3-√2)/(√3+√2)

The denominator = √3+√2

The Rationalising factor of √3+√2 is √3-√2

On Rationalising the denominator then

=> [(√3-√2)/(√3+√2)]×[(√3-√2)/(√3-√2)]

=> [(√3-√2)(√3-√2)]×[(√3+√2)(√3-√2)]

=> (√3-√2)²/[(√3+√2)(√3-√2)]

=> (√3-√2)²/[(√3)²-(√2)²]

Since (a+b)(a-b) = a²-b²

Where , a = √3 and b = √2

=> (√3-√2)²/(3-2)

=> (√3-√2)²/1

=> (√3-√2)²

=> (√3)²-2(√3)(√2)+(√2)²

Since , (a-b)² = a²-2ab+b²

Where , a = √3 and b = √2

=> 3-2√6+2

=> 5-2√6

Hence, the denominator is rationalised.

Answer:

Rationalised form of (√3-√2)/(√3+√2) is 5 - 2√6.

Used formulae:-

  • (a+b)(a-b) = a²-b²
  • (a-b)² = a²-2ab+b²
  • The Rationalising factor of √3+√2 is √3-√2
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