Question

rationalize and explain​

Answer 1

Solution:

Given to Rationalise,

$\tt = \dfrac{1}{1 - 2\sqrt{3} }$

Multiplying both numerator and denominator by the conjugate of denominator, we get,

$\tt = \dfrac{1 \times (1 + 2 \sqrt{3} )}{(1 - 2\sqrt{3})(1 + 2 \sqrt{3}) }$

$\tt = \dfrac{1 + 2 \sqrt{3}}{(1) ^{2} - (2\sqrt{3})^{2}}$

$\tt = \dfrac{1 + 2 \sqrt{3}}{1-12}$

$\tt = \dfrac{1 + 2 \sqrt{3}}{ -11}$

$\tt = \dfrac{ - 1 - 2 \sqrt{3}}{11}$

So, after rationalisation, we get,

$\tt = \dfrac{ - 1 - 2 \sqrt{3}}{11}$

Answer:

• $\tt \dfrac{ - 1 - 2 \sqrt{3}}{11}$

Concept:

• Rationalisation: This is the process to remove the surds from the denominator part of a fraction. To do this, we have to multiply both numerator and denominator part of the fraction with the conjugate of denominator.
• For example, here conjugate of 1 - 2√3 is 1 + 2√3.

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