Toán Lớp 9: Rút gọn: A = ( √ 6 + √ 20 − 2 √ 3 − √ 5 + √ 15 − 10 √ 2 ) : ( 2 + √ 8 )

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1. $A = \left(\sqrt{6+\sqrt{20}}-2\sqrt{3-\sqrt{5}}+\sqrt{15-10\sqrt{2}}\right)\ :\ \left(2+\sqrt8\right)$

   $\to A = \left(\sqrt{\left(\sqrt5\right)^2 +2.\sqrt{5}.1 + 1^2}-\sqrt2.\sqrt{\left(\sqrt5\right)^2-2.\sqrt{5}.1+ 1^2}+\sqrt{\left(\sqrt{10}\right)^2-2.\sqrt{10}\sqrt{5} + \left(\sqrt5\right)^2}\right)\ :\ \left[2\left(1+\sqrt2\right)\right]$

   $\to A = \left[\sqrt{\left(\sqrt5+1\right)^2}-\sqrt2.\sqrt{\left(\sqrt5-1\right)^2}+\sqrt{\left(\sqrt{10}-\sqrt5\right)^2}\right]\ :\ \left[2\left(1+\sqrt2\right)\right]$

   $\to A = \left[\sqrt5 +1 – \sqrt2\left(\sqrt5-1\right) + \left(\sqrt{10}-\sqrt5\right)\right]\ :\ \left[2\left(1+\sqrt2\right)\right]$

   $\to A = \left(1+\sqrt2\right)\ :\ \left[2\left(1+\sqrt2\right)\right]$

   $\to A =\dfrac12$

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