rationalise the denominators of the
following 4+2√3/4-2√3
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rationalise the denominators of the
following 4+2√3/4-2√3
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Given:
To Find:
Answer:
We are here given a number whose denominator we have to rationalise.
Now taking the given number ;
[tex]\sf{\longmapsto\dfrac{4+2\sqrt{3}}{4-2\sqrt{3}}}[/tex]
[tex]\sf{\longmapsto \dfrac{(4+2\sqrt{3})(4+2\sqrt{3})}{(4-2\sqrt{3})(4+2\sqrt{3})}}[/tex]
[tex]\sf{\longmapsto \dfrac{(4+2\sqrt{3})^{2}}{(4)^{2}-(2\sqrt{2})^{2}}}[/tex]
using
[tex]\sf{\longmapsto \dfrac{(4+2\sqrt{3})^{2}}{16-12}}[/tex]
[tex]\sf{\longmapsto \dfrac{16+12+16\sqrt{2}}{4}}[/tex]
using
[tex]\sf{\longmapsto \dfrac{28+16\sqrt{2}}{4}}[/tex]
[tex]\sf{\longmapsto 4\dfrac{(7+4\sqrt{2})}{4}}[/tex]
[tex]\sf{\longmapsto 7+4\sqrt{2}}[/tex]