Question

rationalise the denominators of the
following 4+2√3/4-2√3​

Answer 1

Given:

• A number is given to us i.e.$\sf{\dfrac{4+2\sqrt{3}}{4-2\sqrt{3}}}$

To Find:

• The number after rationalising the denominator.

Answer:

We are here given a number whose denominator we have to rationalise.

Now taking the given number ;

$\sf{\longmapsto\dfrac{4+2\sqrt{3}}{4-2\sqrt{3}}}$

$\sf{\longmapsto \dfrac{(4+2\sqrt{3})(4+2\sqrt{3})}{(4-2\sqrt{3})(4+2\sqrt{3})}}$

$\sf{\longmapsto \dfrac{(4+2\sqrt{3})^{2}}{(4)^{2}-(2\sqrt{2})^{2}}}$

using

• (a+b)(a-b)=a²-b²

$\sf{\longmapsto \dfrac{(4+2\sqrt{3})^{2}}{16-12}}$

$\sf{\longmapsto \dfrac{16+12+16\sqrt{2}}{4}}$

using

• (a+b)²=a²+b²+2ab

$\sf{\longmapsto \dfrac{28+16\sqrt{2}}{4}}$

$\sf{\longmapsto 4\dfrac{(7+4\sqrt{2})}{4}}$

$\sf{\longmapsto 7+4\sqrt{2}}$