1 thực hienj phép tính 4. rút gọn\(\sqrt{\left(3-\sqrt{10}\right)^2}+\sqrt{\left(2\sqrt{10}-6\right)^2}\) \(x\sqrt{\frac{9}{x}}+5\sqrt{x}\left(x>0\right)\)2, tính \(\sqrt{2}.\sqrt{18};\frac{\sqrt{108a}}{\sqrt{3a}}\left(a>0\right)\) ...
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1 thực hienj phép tính 4. rút gọn
\(\sqrt{\left(3-\sqrt{10}\right)^2}+\sqrt{\left(2\sqrt{10}-6\right)^2}\) \(x\sqrt{\frac{9}{x}}+5\sqrt{x}\left(x>0\right)\)
2, tính \(\sqrt{2}.\sqrt{18};\frac{\sqrt{108a}}{\sqrt{3a}}\left(a>0\right)\)
: \(2\sqrt{56}-14\sqrt{\frac{2}{7}}\left(\sqrt{7}-\sqrt{2}\right)\sqrt{7}-\frac{8\sqrt{2}}{\sqrt{3}-\sqrt{7}}\) (tính giá trị)
1. Ta có: \(9< 10\)\(\Rightarrow\sqrt{9}< \sqrt{10}\)\(\Rightarrow3< \sqrt{10}\)\(\Rightarrow3-\sqrt{10}< 0\)(1)
Vì \(3< \sqrt{10}\)\(\Rightarrow2.3< 2\sqrt{10}\)\(\Rightarrow6< 2\sqrt{10}\)\(\Rightarrow2\sqrt{10}-6>0\)(2)
Từ (1) và (2) \(\Rightarrow\sqrt{\left(3-\sqrt{10}\right)^2}+\sqrt{\left(2\sqrt{10}-6\right)^2}\)
\(=\left|3-\sqrt{10}\right|+\left|2\sqrt{10}-6\right|\)
\(=\sqrt{10}-3+2\sqrt{10}-6=3\sqrt{10}-9\)
4. Vì \(x>0\)\(\Rightarrow x.\sqrt{\frac{9}{x}}+5\sqrt{x}=\sqrt{x^2.\frac{9}{x}}+5\sqrt{x}=\sqrt{9x}+5\sqrt{x}\)
\(=3\sqrt{x}+5\sqrt{x}=8\sqrt{x}\)