\(\sqrt{8-2\sqrt{15}}+\sqrt{8+2\sqrt{15}}\)
\(=\sqrt{5-2\sqrt{3}\sqrt{5}+3}+\sqrt{5+2\sqrt{3}\sqrt{5}+3}\)
\(=\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}\)
\(=\sqrt{5}-\sqrt{3}+\sqrt{5}+\sqrt{3}\)
\(=2\sqrt{5}\)
\(\sqrt{8-2\sqrt{15}}+\sqrt{8+2\sqrt{15}}\)
\(=\sqrt{5-2\sqrt{3}\sqrt{5}+3}+\sqrt{5+2\sqrt{3}\sqrt{5}+3}\)
\(=\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}\)
\(=\sqrt{5}-\sqrt{3}+\sqrt{5}+\sqrt{3}\)
\(=2\sqrt{5}\)
Rút gọn \(A=\sqrt{8+2\cdot\sqrt{10+2\cdot\sqrt{5}}}+\sqrt{8-2\cdot\sqrt{10-2\cdot\sqrt{5}}}\)
Tính
a) \(\sqrt{6-\sqrt{11}}\cdot\sqrt{6+\sqrt{11}}\)
b) \(\sqrt{8+\sqrt{15}}\cdot\sqrt{8-\sqrt{15}}\)
Rút gọn \(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
giúp mk mới mọi người ơi
câu 1 rút gọn
a .\(2.\sqrt{48}+\sqrt{27}+\sqrt{3}\)
b\(\sqrt{45.a^2}+\sqrt{8.b^2}+5\cdot\sqrt{5\cdot a\cdot a^2}-3\cdot b\cdot\sqrt{2\cdot b}\)
TÍNH :
\(A=\sqrt{3+\sqrt{5+2\sqrt{3}}}\cdot\sqrt{3-\sqrt{5+2\sqrt{3}}}\)
\(B=\sqrt{4+\sqrt{8}}\cdot\sqrt{2+\sqrt{2+\sqrt{2}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2}}}\)
\(C=\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
\(D=\left[4+\sqrt{15}\right]\left[\sqrt{10}-\sqrt{6}\right]\cdot\sqrt{4-\sqrt{15}}\)
\(E=\left[3-\sqrt{5}\right]\cdot\sqrt{3+\sqrt{5}}\text{ }+\left[3+\sqrt{5}\right]\cdot\sqrt{3-\sqrt{5}}\)
cho số thực a<1. Rút gọn biểu thức \(P=\sqrt{\frac{15}{2}}\cdot\sqrt{\frac{10\cdot\left(a-1\right)^2}{3}}\)
\(\left(\frac{4\cdot\sqrt{x}}{2+\sqrt{x}}\right)+\left(\frac{8\cdot x}{4-x}\right)\) rút gọn giúp mình với
rút gọn hộ mik vs
4)\(\sqrt{8+2\sqrt{15}}\) -\(\sqrt{8-2\sqrt{15}}\)
5)\(\sqrt{5+2\sqrt{6}}\) +\(\sqrt{8-2\sqrt{15}}\)
\(\sqrt{\frac{5\cdot\left(38^2-17^2\right)}{8\cdot\left(47^2-19^2\right)}}\)cái này rút gọn nha
\(\sqrt{x^2-6x+9}=\sqrt{4+2\sqrt{3}}\)cái này giải phương trình haaaaaa