Answered

IDNLearn.com makes it easy to find answers and share knowledge with others. Ask anything and receive thorough, reliable answers from our community of experienced professionals.

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

Sagot :

SalmonWorldTopperidn

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
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.