Math, asked by shaanaasim1234, 8 months ago

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

Answers

Answered by Anonymous
67

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}}

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