Question

rationalize the denominator 3/√6-√7​

Answer 1

Answer:

The answer is -3(√6+√7)

Step-by-step explanation:

• 3/√6-√7 × √6+√7/ √6+√7
• = 3√6 + 3√7 / (√6)²- (√7)²
• Identity (a+b) (a-b) = ( a²- b² )
• 3(√6 + √7) / (6-7)
• = 3(√6+√7) / -1
• = -3(√6+√7)

In rationalization the sign of the denominator change when it went in numerator

for ex. . + sign changes into -

and - sign changes into +

Answer 2

Given : 3/(√6 - √7)

$\dfrac{3}{ \sqrt{6} - \sqrt{7} }$

To Find : rationalize the denominator

Solution:

$\dfrac{3}{ \sqrt{6} - \sqrt{7} }$

Denominator is √6 - √7

Rationalizing factor will be √6  + √7

Multiply and divide by Rationalizing factor

$=\dfrac{3}{ \sqrt{6} - \sqrt{7} } \times\dfrac{\sqrt{6} + \sqrt{7}}{ \sqrt{6} + \sqrt{7} }$

Using identity  (a + b)(a - b)  = a² - b²

and (√a)² = a

$=\dfrac{3(\sqrt{6} + \sqrt{7})}{ 6 -7 }$

$=\dfrac{3(\sqrt{6} - \sqrt{7})}{ -1 }$

$= -3(\sqrt{6} + \sqrt{7})$

Hence Answer is - 3(√6 + √7)

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