rút gọn \(\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
rút gọn
\(\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
\(\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
\(=\sqrt{1+2+5+2\left(\sqrt{2}+\sqrt{5}+\sqrt{10}\right)}=\sqrt{\left(1+\sqrt{2}+\sqrt{5}\right)^2}\)
\(=1+\sqrt{2}+\sqrt{5}\)
\(\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
Rút gọn Bt
Rút gọn biểu thức :
\(A=\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}.}\)
\(A=\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}=\sqrt{\sqrt{5}^2+\sqrt{2}^2+1^2+2\sqrt{2}.1}+2\sqrt{5}.1+2\sqrt{2}\sqrt{5}}\)
=\(\sqrt{\left(\sqrt{5}+\sqrt{2}+1\right)^2=\sqrt{5}+\sqrt{2}+1}\)
Rút gọn biểu thức sau
\(\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
Rút gọn biểu thức sau
\(A=\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
\(A=\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
\(=\sqrt{\sqrt{5}^5+\sqrt{2}^2+1^2+2\sqrt{2}.1+2\sqrt{2}.\sqrt{5}}\)
\(=\sqrt{\left(\sqrt{5}+\sqrt{2}+1\right)^2}\)
\(=\sqrt{5}+\sqrt{2}+1\)
=√√55+√22+12+2√2.1+2√2.√5
=√(√5+√2+1)2
1. Rút gọn A= \(\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
2. Tính : \(\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+...}}}}}\)
\(A=\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+....}}}}>0\)
\(\Rightarrow A^2=6+\sqrt{6+\sqrt{6+\sqrt{6+....}}}\)
\(\Rightarrow A^2=6+A\)\(\Rightarrow A^2-A-6=0\)
\(\Rightarrow\left(A-3\right)\left(A+2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}A-3=0\\A+2=0\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}A=3\\A=-3\end{cases}}\Rightarrow A=3>0\) (thỏa)
câu 1 mình làm được rồi! mik cần mọi người help mình câu 2 ! pleaseeeeee.......... T-T
Rút gọn biểu thức
\(2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}-3\sqrt{5\sqrt{48}}}\)
\(2\sqrt{5\sqrt{3}}-2\sqrt{8\sqrt{3}}-3\sqrt{20\sqrt{3}}\)
Help me plsssssss
Help me plssssssss
a: \(=2\sqrt{20\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\cdot\sqrt{20\sqrt{3}}\)
\(=4\sqrt{5\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{3}}=-4\sqrt{5\sqrt{3}}\)
b: \(=2\sqrt{5\sqrt{3}}-4\sqrt{2\sqrt{3}}-6\sqrt{5\sqrt{3}}=-4\sqrt{5\sqrt{3}}-4\sqrt{2\sqrt{3}}\)
Rút gọn bt
\(a,A=\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
\(b,B=\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}+11\right)\)
\(a,A=\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
\(=\sqrt{\left(\sqrt{5}^2+2\sqrt{5}+2\sqrt{2}\cdot\sqrt{5}\right)+\sqrt{2}^2+2\sqrt{2}\cdot1+1^2}\)
\(=\sqrt{\sqrt{5}^2+2\cdot\sqrt{5}\left(\sqrt{2}+1\right)+\left(\sqrt{2}+1\right)^2}\)
\(=\sqrt{\left(\sqrt{5}+\sqrt{2}+1\right)^2}\)
\(=\sqrt{5}+\sqrt{2}+1\)
\(b,B=\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}+11\right)\)
\(=\left(\frac{3\cdot\left(\sqrt{6}+1\right)\left(\sqrt{6}-1\right)}{\sqrt{6}+1}+\frac{2\left(\sqrt{6}-2\right)\left(\sqrt{6}+2\right)}{\sqrt{6}-2}-\frac{4\left(3-\sqrt{6}\right)\left(3+\sqrt{6}\right)}{3-\sqrt{6}}\right)\left(\sqrt{6}+11\right)\)
\(=\left[3\cdot\left(\sqrt{6}-1\right)+2\left(\sqrt{6}+2\right)-4\left(3+\sqrt{6}\right)\right]\left(\sqrt{6}+11\right)\)
\(=\left(\sqrt{6}+11\right)\left(\sqrt{6}-11\right)=-115\)
Rút gọn
\(2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}\)
\(2\sqrt{8\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{20\sqrt{3}}\)