Kak yg cantik cakep pinter dan anak soleh ngerjain soal dibwh ini!!! simptify the following roots !!.... Question from @felialex

October 2018 2 23 Report

Kak yg cantik cakep pinter dan anak soleh ngerjain soal dibwh ini!!!

simptify the following roots !!
a. $\sqrt{7+2 \sqrt{12} }$
b $\sqrt{10-2 \sqrt{24} }$
c. $\sqrt{16+\sqrt{220} }$

Brillianttt √7+2√12 = √((4+3) + 2√4x3) = √4 + √2 = 2 + √3

√10+2√24 = √((6+4)+2√(6x4) = √6+√4 = √6 + 2\

√16 + √220 = √16+√4x55 = √16+2√55 = √((11+5)+2√11x5 = √11 + √5

1 votes Thanks 3

Takamori37 Rumus untuk ini adalah:
$\boxed{\sqrt{(a+b)\pm2\sqrt{a\times b}}=\sqrt a\pm \sqrt b}$

Sehingga:
$$\begin{align}\sqrt{7+2\sqrt{12}}&=\sqrt{(4+3)+2\sqrt{4\times3}} \\ &=\sqrt4+\sqrt3 \\ &=2+\sqrt3 \\\\ \sqrt{10-2\sqrt{24}}&=\sqrt{(6+4)-2\sqrt{6\times4}} \\ &=\sqrt6-\sqrt4 \\ &=\sqrt6-2 \\\\ \sqrt{16+\sqrt{220}}&=\sqrt{16+\sqrt{4\times55}} \\ &=\sqrt{16+2\sqrt{55}} \\ &=\sqrt{(11+5)+2\sqrt{11\times5}} \\ &=\sqrt{11}+\sqrt{5}\end{align}$

1 votes Thanks 0

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