$\dfrac{4\pm\sqrt{28}}{2}=2\pm\sqrt7$
My Question is how did $\dfrac{4\pm\sqrt{28}}{2}$ become simplified as $2\pm\sqrt7$
Can you help me by explaining the steps clearly
:) Many Thanks
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Notice that $\sqrt{28}=\sqrt{4\times7}=\sqrt{4}\times\sqrt{7}=2\sqrt{7}$.
Hence $\dfrac{4\pm\sqrt{28}}{2}=\dfrac{4\pm2\sqrt{7}}{2}=\dfrac{2(2\pm\sqrt{7})}{2}=2\pm\sqrt{7}$.
Ian Miller
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blastzit
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ok then the 4 on top and the 2 on the denominator aren't they simplified? – user360471 Aug 11 '16 at 06:54
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@user360471 Hopefully that edit makes it a bit clearer what happened to the 2 and the 4. – Ian Miller Aug 11 '16 at 07:29
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$\dfrac{4\pm\sqrt{28}}{2}=$
$\dfrac{4\pm\sqrt{4\cdot7}}{2}=$
$\dfrac{4\pm\sqrt{4}\cdot\sqrt{7}}{2}=$
$\dfrac{4\pm2\cdot\sqrt{7}}{2}=$
$\dfrac{2\pm1\cdot\sqrt{7}}{1}=$
$2\pm\sqrt{7}$
barak manos
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I admire your patience in explaining elementary stuff in such details. +1 – P Vanchinathan Aug 11 '16 at 07:56
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@PVanchinathan: Haha, not much patience was required in this case :) – barak manos Aug 11 '16 at 08:09