Question

Rationalise the denominator 1÷2+√3

if your answer is useless I will report you and you will lose 50 points​

Answer 1

Answer :

= 2 - √3

Step-by-step explanation :

$\underline{\bf Rationalizing \ factor:}$

• The factor of multiplication by which rationalization is done, is called as rationalizing factor.

• If the product of two surds is a rational number, then each surd is a rationalizing factor to other.

• To find the rationalizing factor,

          =>  If the denominator contains 2 terms, just change the sign between the two terms.

              For example, rationalizing factor of (3 + √2) is (3 - √2)

          => If the denominator contains 1 term, the radical found in the denominator is the factor.

              For example, rationalizing factor of √2 is √2

____________________________

Given fraction,

$\bf =\frac{1}{2+\sqrt{3}}$

Rationalizing factor = 2 - √3

=> Multiply and divide the given fraction by the rationalizing factor.

   $\bf =\frac{1}{2+\sqrt{3}} \times \frac{2-\sqrt{3}}{2-\sqrt{3}} \\\\\\ =\frac{1(2-\sqrt{3})}{(2+\sqrt{3})(2-\sqrt{3})} \\\\\\ = \frac{2-\sqrt{3}}{2(2-\sqrt{3})+\sqrt{3}(2-\sqrt{3})} \\\\\\ = \frac{2-\sqrt{3}}{4-2\sqrt{3}+2\sqrt{3}-\sqrt{3}^2} \\\\\\ = \frac{2-\sqrt{3}}{4-3} \\\\\\ = \frac{2-\sqrt{3}}{1} \\\\\\ =2-\sqrt{3}$