Question

Rationalize denominator 3/root5-6​

Answer 1

Question -

↬ Rationalize the denominator.

• $\sf{\dfrac{3}{\sqrt{5- 6}}}$

Solution -

↬ $\sf{\dfrac{3}{\sqrt{5- 6}}}$

↬ $\sf{\dfrac{3 \times \sqrt{5 } + 6}{\sqrt{5 - 6} \times \sqrt{5 + 6} }}$

↬ $\sf{\dfrac{3 \times \sqrt{5 } + 6}{ \bigg(\sqrt{5 - 6} \bigg)^{2}}}$

↬ $\sf{\dfrac{3 \times \sqrt{5 + 6 }}{ 5 - 6 }}$

↬ $\sf{\dfrac{3\sqrt{5 + 6}}{ - 1}}$

How to solve?

↬

To rationalize the denominator-

• Firstly, multiply both the denominator and numerator with conjugate of the denominator.
• [conjugate - Same terms but different signs.]
• Use identities as the denominator is same now.
• Identity -

↬ $\sf{(a - b)(a + b) = a^2 - b^2}$

• Then multiply and we're done now.