A= ( \(\sqrt{1}\)+\(\sqrt{2}\)+\(\sqrt{3}\) ) + (\(\sqrt{20}\) + \(\sqrt{40}\) + \(\sqrt{60}\))
= (1+1,4+1,7)+(4,4+6,3+7,7)
= 4,1+18,4
=22,5
Chứng minh rằng:
a) \(\sqrt{1}+\sqrt{2}+\sqrt{3}+...+\sqrt{8}< 24\)
b) \(\dfrac{1}{\sqrt{1}}+\dfrac{1}{\sqrt{2}}+...+\dfrac{1}{\sqrt{100}}>10\)
c) \(\sqrt{6}+\sqrt{12}+\sqrt{20}+\sqrt{30}+\sqrt{42}+\sqrt{50}< 30\)
so sánh
\(\sqrt{21}-\sqrt{5}và\sqrt{20-\sqrt{6}}\)
Chứng tỏ
\(a,\sqrt{21}-\sqrt{5}>\sqrt{20}-\sqrt{6
}\)
\(b,\sqrt{2}+\sqrt{8}< \sqrt{3}+3\)
c,\(\sqrt{5}+\sqrt{10}>5,3\)
So sánh
a)\(\sqrt{21}+\sqrt{5}\) và \(\sqrt{20}-\sqrt{6}\)
b)\(\frac{\sqrt{5^2}+\sqrt{35^2}}{\sqrt{7^2}+\sqrt{49^2}}\) và \(\frac{\sqrt{5^2}-\sqrt{35^2}}{\sqrt{7^2}-\sqrt{49^2}}\)
So sánh:
\(A=\sqrt{2}+\sqrt{6}+\sqrt{12}+\sqrt{20}+\sqrt{30}+\sqrt{42}\)
B=24
So Sánh \(A=\sqrt{2}+\sqrt{6}+\sqrt{12}+\sqrt{20}+\sqrt{30}+\sqrt{42}\)
Và\(B=24\)
Tính:
a) \(\sqrt{27}+\sqrt{75}-\sqrt{\dfrac{1}{3}}\)
b) \(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)
c) \(\dfrac{3}{\sqrt{7}+\sqrt{2}}+\dfrac{2}{3+\sqrt{7}}+\dfrac{2-\sqrt{2}}{\sqrt{2}-1}\)
Bài 1Trong các số sau đây số nào bằng \(\dfrac{3}{5}\)
a,\(\sqrt{\dfrac{3^2}{5^2}}\)
b,\(\dfrac{\sqrt{3^2}+\sqrt{42^2}}{\sqrt{5^2}+\sqrt{70^2}}\)
c,\(\dfrac{\sqrt{3^2}-\sqrt{8^2}}{\sqrt{5^2}-\sqrt{8^2}}\)
Bài 2
a, \(x=\sqrt{3}+\sqrt{6}\)
\(y=2\sqrt{3}\)
b,\(x=\sqrt{3}+\sqrt{6}\)
\(y=\sqrt{2}+\sqrt{7}\)
c,\(x=-\dfrac{1}{2}\sqrt{\dfrac{1}{3}}\)
\(y=-\dfrac{1}{3}\sqrt{\dfrac{1}{2}}\)
Bài 3
\(a,\sqrt{x}-1=4\)
\(b,\sqrt{\left(x-1\right)^4}=16\)
So sánh: A= \(\sqrt{2}\)+\(\sqrt{6}\)+\(\sqrt{12}\)+\(\sqrt{20}\)+\(\sqrt{30}\)+\(\sqrt{42}\)
và B=24