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a) \(\sqrt{75}+\sqrt{48}-\sqrt{300}\) = \(5\sqrt{3}+4\sqrt{3}-10\sqrt{3}\) = \(-\sqrt{3}\)
b) \(\sqrt{98}-\sqrt{72}+0,5\sqrt{8}\) = \(7\sqrt{2}-6\sqrt{2}+\sqrt{2}\) = \(2\sqrt{2}\)
c) \(\sqrt{9a}-\sqrt{16a}+\sqrt{49a}\) = \(3\sqrt{a}-4\sqrt{a}+7\sqrt{a}\) = \(6\sqrt{a}\)
d) \(\sqrt{16b}+2\sqrt{40b}-3\sqrt{90b}\) = \(4\sqrt{b}+4\sqrt{10b}-9\sqrt{10b}\)
= \(4\sqrt{b}-5\sqrt{10b}\)
1) \(\sqrt{9a}-\sqrt{16a}+\sqrt{49a}\left(a\ge0\right)\)\(=3\sqrt{a}-4\sqrt{a}+7\sqrt{a}\) \(=6\sqrt{a}\)
2) \(2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{80}}\)
= \(2\sqrt{80\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{20\sqrt{5}}\)
= \(8\sqrt{5\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{5}}\)
= \(6\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{5}}\)
3) \(\dfrac{\sqrt{x^3}-1}{\sqrt{x}-1}\) = \(\dfrac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}-1}\) = \(x+\sqrt{x}+1\)
4) \(\sqrt{16b}+2\sqrt{40b}-3\sqrt{90b}\)
\(=\sqrt{4^2\cdot b}+2\sqrt{2^2\cdot10b}-3\sqrt{3^2\cdot10b}\)
\(=4\sqrt{b}+2\cdot2\sqrt{10b}-3\cdot3\sqrt{10b}\)
\(=4\sqrt{b}+4\sqrt{10b}-9\sqrt{10b}\)
\(=4\sqrt{b}+\left(4\sqrt{10b}-9\sqrt{10b}\right)\)
\(=4\sqrt{b}-5\sqrt{10b}\)
`a, sqrt(16b) + 2 sqrt(40b) - 3 sqrt(90b)`
`= 4sqrtb + 2sqrt(8.5b) - 3 sqrt(9.10b)`
`= 4 sqrt b + 4sqrt(10b) - 9 sqrt(10b)`
`= 4sqrtb-5sqrt(10b)`.
2) \(\sqrt{98}-\sqrt{72}+0,5\sqrt{8}\)
\(=7\sqrt{2}-6\sqrt{2}+\sqrt{2}\)
\(=\left(7-6+1\right)\sqrt{2}\)
\(=2\sqrt{2}\)
3) \(\sqrt{9a}-\sqrt{16a}+\sqrt{49a}\)
\(=3\sqrt{a}-4\sqrt{a}+7\sqrt{a}\)
\(=\left(3-4+7\right)\sqrt{a}\)
\(=6\sqrt{a}\)
4) \(\sqrt{16b}+2\sqrt{40b}-3\sqrt{90b}\)
\(=4\sqrt{b}+4\sqrt{10b}-9\sqrt{10b}\)
\(=4\sqrt{b}-5\sqrt{10b}\)
Gấp nha