Question

Rationalize denominator​

Answer 1

Step-by-step explanation:

Question:—

• If √5+√6/√5-√6 = a+b√30, then find the value of a and b ?

To find:—

• the value of a and b ?

Solution:—

Let's solve the given problem

We have,

$\mathrm{ \frac{ \sqrt{5} + \sqrt{6} }{ \sqrt{5} - \sqrt{6} } = a + b \sqrt{30} }$

The denominator is √5-√6. Multiplying the numerator and denomination by √5+√6, we get

$⟹ \frac{ \sqrt{5} + \sqrt{6} }{ \sqrt{5} - \sqrt{6} } \times \frac{ \sqrt{5} + \sqrt{6} }{ \sqrt{5} + \sqrt{6} }$

$⟹ \frac{( \sqrt{5} + \sqrt{6} )( \sqrt{5} + \sqrt{6} ) }{( \sqrt{5} - \sqrt{6})( \sqrt{5} + \sqrt{6}) }$

⬤ Applying Algebraic Identity

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

We get,

$⟹ \frac{( \sqrt{5} + \sqrt{6} {)}^{2} }{( \sqrt{5} {)}^{2} - ( \sqrt{6} {)}^{2} }$

$⟹ \frac{( \sqrt{5} {)}^{2} + ( \sqrt{6} {)}^{2} + 2 \sqrt{5} \: \sqrt{6} }{3 - 2}$

$⟹ \frac{5 + 6 + 2 \sqrt{5} \: \sqrt{6} }{3 - 2}$

$⟹ \frac{11 + 2 \sqrt{5 \times 6} }{1}$

$⟹ \frac{11 + 2 \sqrt{30} }{1}$

$⟹11 + 2 \sqrt{30}$

$.°. \: a + b \sqrt{30} = 11 + 2 \sqrt{30}$

On comparing the value of

a = 11 and b = 2

Answer:—

• Hence, the value of a = 11 and b = 2

Used Formulae:—

• a+b)(a+b) = (a+b)² = a² + b² + 2ab
• (a-b)(a+b) = a² - b²

# Brainly

Learn more:

If (√2+1)²/3-√2 = a+b√3 , find a and b.

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