Question

Rationalise the dinomenator √5-2/√5+2 X√5/√5



What is the Answer​

Answer 1

Step-by-step explanation:

Correct Question:-

Rationalise the dinomenator √5-2/√5+2

Solution:-

Let's solve the problem

We have,

√5 - 2/ √5 + 2

The denominator is √5+2. Multiplying the numerator and denomination by √5-2, we get

=> √5-2/√5+2 × √5-2/√5-2

=> (√5-2)(√5-2)/(√5+2)(√5+2)

⬤ Applying Algebraic Identity

1. (a-b)² = a² + b² - 2ab to the numerator and
2. (a+b)(a-b) = a² - b² to the denominator

We get,

=> (√5-2)²/(√5)²-(2)²

=> (√5)² + (2)² - 2 × √5 × 2 / 5 - 4

=> 5 + 4 - 4√5 /1

=> 9 - 4√5.

Hence, the denominator is rationalised.

Answer:-

• 9 - 4√5

Used formulae:-

• (a - b)² = a² + b² - 2ab

• (a+b)(a-b) = a² - b²

Answer 2

Answer:

Rationalise the dinomenator √5-2/√5+2

Solution:-

Let's solve the problem

We have,

√5 - 2/ √5 + 2

The denominator is √5+2. Multiplying the numerator and denomination by √5-2, we get

=> √5-2/√5+2 × √5-2/√5-2

=> (√5-2)(√5-2)/(√5+2)(√5+2)

⬤ Applying Algebraic Identity

(a-b)² = a² + b² - 2ab to the numerator and

(a+b)(a-b) = a² - b² to the denominator

We get,

=> (√5-2)²/(√5)²-(2)²

=> (√5)² + (2)² - 2 × √5 × 2 / 5 - 4

=> 5 + 4 - 4√5 /1

=> 9 - 4√5.

Hence, the denominator is rationalised.

Answer:-

9 - 4√5

Used formulae:-

(a - b)² = a² + b² - 2ab

(a+b)(a-b) = a² $b^{2}$

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Step-by-step explanation: