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\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\left(\sqrt{4-\sqrt{15}}\right)\)
\(=\left(4\sqrt{10}-4\sqrt{6}+5\sqrt{6}-3\sqrt{10}\right)\left(\sqrt{\frac{5}{2}}-\sqrt{\frac{3}{2}}\right)\)
\(=\left(\sqrt{10}+\sqrt{6}\right)\left(\sqrt{\frac{5}{2}}-\sqrt{\frac{3}{2}}\right)\)
\(=5-\sqrt{15}+\sqrt{15}-3=2\)
(Nếu đúng thì click cho mình 1 cái nhe!)
mình không hiểu chỗ : \(\sqrt{\frac{5}{2}}-\sqrt{\frac{3}{2}}\)
\(A=\dfrac{10.\sqrt{18}+5\sqrt{3}-15\sqrt{27}}{\sqrt{3}.\left(\sqrt{6}-4\right)}\)
\(A=\dfrac{10.\sqrt{3.6}+5\sqrt{3}-15.\sqrt{3.3^2}}{\sqrt{3}.\left(\sqrt{6}-4\right)}\)
\(A=\dfrac{10.\sqrt{3}.\sqrt{6}+5\sqrt{3}-15.\sqrt{3}.3}{\sqrt{3}\left(\sqrt{6}-4\right)}\)
\(A=\dfrac{\sqrt{3}.\left(10.\sqrt{6}+5-15.3\right)}{\sqrt{3}\left(\sqrt{6}-4\right)}\)
\(A=\dfrac{10.\sqrt{6}+5-45}{\sqrt{6}-4}=\dfrac{10.\sqrt{6}-40}{\sqrt{6}-4}\)
\(A=\dfrac{10.\left(\sqrt{6}-4\right)}{\sqrt{6}-4}=10\)
Vậy \(A=10\)
Chúc bạn học tốt!!!
a) \(\sqrt{\left(4-\sqrt{15}\right)^{2^{ }}}+\sqrt{15}\)
=\(\left|4-\sqrt{15}\right|+\sqrt{15}\)
= \(4-\sqrt{15}+\sqrt{15}\) ( vì 4 =\(\sqrt{16}\) mà \(\sqrt{16}>\sqrt{15}\) )
=4
b)\(\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(1-\sqrt{3}\right)^2}\)
=\(\left|2-\sqrt{3}\right|+\left|1-\sqrt{3}\right|\) ( vì \(1< \sqrt{3}< 2\))
= \(2-\sqrt{3}-1+\sqrt{3}\)
=1
a) Ta có: \(\sqrt{\left(4-\sqrt{15}\right)^2}+\sqrt{15}\)
\(=\left|4-\sqrt{15}\right|+\sqrt{15}\)
\(=4-\sqrt{15}+\sqrt{15}\)
=4
b) Ta có: \(\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(1-\sqrt{3}\right)^2}\)
\(=\left|2-\sqrt{3}\right|+\left|1-\sqrt{3}\right|\)
\(=2-\sqrt{3}+\sqrt{3}-1\)
\(=1\)
\(=\frac{-40\sqrt{3}+30\sqrt{2}}{-4\sqrt{3}+3\sqrt{2}}=10\)
\(C=\left(4+\sqrt{15}\right)\cdot\left(\sqrt{5}-\sqrt{3}\right)\cdot\sqrt{8-2\sqrt{15}}\)
\(=\left(4+\sqrt{15}\right)\left(8-2\sqrt{15}\right)\)
\(=32-8\sqrt{15}+8\sqrt{15}-30=2\)
`C=(4+\sqrt{15})(\sqrt{10}-\sqrt{6})\sqrt{4-\sqrt{15}}`
`C=(4\sqrt{10}-4\sqrt{6}+5\sqrt{6}-3\sqrt{10})\sqrt{4-\sqrt{15}}`
`C=(\sqrt{10}+\sqrt{6})\sqrt{4-\sqrt{15}}`
`C=\sqrt{(\sqrt{10}+\sqrt{6})^2 .(4-\sqrt{15})}`
`C=\sqrt{(10+6+2\sqrt{60})(4-\sqrt{15})}`
`C=\sqrt{(16+4\sqrt{15})(4-\sqrt{15})}`
`C=\sqrt{64-16\sqrt{15}+16\sqrt{15}-60}`
`C=\sqrt{4}=2`