Thực hiện phép tính
a) \(\left(3-\sqrt{3}\right)\left(-2\sqrt{3}\right)+\left(3\sqrt{3}+1\right)^2\)
b) \(\left(3\sqrt{5}-2\sqrt{3}\right).\sqrt{5}+\sqrt{60}\)
Bạn nào bt lm thì giúp Đạt nhé! Thanks!
Thực hiện phép tính
a)\(\sqrt{\left(\sqrt{2}-1\right)^2}+\sqrt{\left(3\sqrt{2}-2\right)^2}\)
b)\(2.\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{\left(2\sqrt{3}+1\right)^2}\)
c)\(4.\sqrt{\left(2-\dfrac{\sqrt{3}}{2}\right)^2}-3.\sqrt{\left(\sqrt{3}-1\right)^2}\)
d)\(\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}\)
e)\(\left(\sqrt{3}-1\right)^2+\left(2\sqrt{3}+1\right)^2\)
g)\(\left(1-2\sqrt{2}\right)^2-\left(\sqrt{2}+1\right)^2\)
a, \(\sqrt{\left(\sqrt{2}-1\right)^2}+\sqrt{\left(3\sqrt{2}-2\right)^2}\)
\(=\left|\sqrt{2}-1\right|+\left|3\sqrt{2}-2\right|\)
\(=\sqrt{2}-1+3\sqrt{2}-2=4\sqrt{2}-3\)
b, \(2\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{\left(2\sqrt{3}+1\right)^2}\)
\(=2\left|\sqrt{3}-1\right|-\left|2\sqrt{3}+1\right|\)
\(=2\sqrt{3}-2-2\sqrt{3}-1=-3\)
c, \(4\sqrt{\left(2-\dfrac{\sqrt{3}}{2}\right)^2}-3\sqrt{\left(\sqrt{3}-1\right)^2}\)
\(=4\left|2-\dfrac{\sqrt{3}}{2}\right|-3\left|\sqrt{3}-1\right|\)
\(=8-2\sqrt{3}-3\sqrt{3}+3=11-5\sqrt{3}\)
d, \(\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}\)
\(=\sqrt{\left(\sqrt{2}+1\right)^2}+\sqrt{\left(\sqrt{2}-1\right)^2}\)
\(=\left|\sqrt{2}+1\right|+\left|\sqrt{2}-1\right|\)
\(=\sqrt{2}+1+\sqrt{2}-1=2\sqrt{2}\)
thực hiện phép tính
a)\(\dfrac{3}{5}\)-\(\dfrac{1}{2}\)\(\sqrt{1\dfrac{11}{25}}\)
b)(5+2\(\sqrt{6}\))(5-2\(\sqrt{6}\))
c)\(\sqrt{\left(2-\sqrt{3}\right)^2}\)+\(\sqrt{4-2\sqrt{3}}\)
d)\(\dfrac{\left(x\sqrt{y}+y\sqrt{x}\right)\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}\)(với x,y>0)
\(a,\dfrac{3}{5}-\dfrac{1}{2}\sqrt{1\dfrac{11}{25}}=\dfrac{3}{5}-\dfrac{1}{2}\sqrt{\dfrac{36}{25}}=\dfrac{3}{5}-\dfrac{1}{2}.\dfrac{\sqrt{6^2}}{\sqrt{5^2}}=\dfrac{3}{5}-\dfrac{1}{2}.\dfrac{6}{5}=\dfrac{3}{5}-\dfrac{6}{10}=\dfrac{3}{5}-\dfrac{3}{5}=0\)
\(b,\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)=5^2-\left(2\sqrt{6}\right)^2=25-2^2.\sqrt{6^2}=25-4.6=25-24=1\)
\(c,\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{4-2\sqrt{3}}\\ =\left|2-\sqrt{3}\right|+\sqrt{\sqrt{3^2}-2\sqrt{3}+1}\\ =2-\sqrt{3}+\sqrt{\left(\sqrt{3}-1\right)^2}\\ =2-\sqrt{3}+\left|\sqrt{3}-1\right|\\ =2-\sqrt{3}+\sqrt{3}-1\\ =1\)
\(d,\dfrac{\left(x\sqrt{y}+y\sqrt{x}\right)\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}\left(dk:x,y>0\right)\\ =\dfrac{\left(\sqrt{x^2}.\sqrt{y}+\sqrt{y^2}.\sqrt{x}\right)\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}\\ =\dfrac{\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}\\ =\sqrt{x^2}-\sqrt{y^2}\\ =\left|x\right|-\left|y\right|\\ =x-y\)
Thực hiện phép tính
a) \(\left(3-\sqrt{3}\right)\left(-2\sqrt{3}\right)+\left(3\sqrt{3}+1\right)^2\)
b) \(\left(3\sqrt{5}-2\sqrt{3}\right).\sqrt{5}+\sqrt{60}\)
c) \(\left(\sqrt{28}-2\sqrt{3}+\sqrt{7}\right).\sqrt{7}+\sqrt{84}\)
- Bạn nào giúp mình với, mình cảm ơn nhìu ...!
* Thực hiện phép tính
a. \(\sqrt{\left(3-\sqrt{2}\right)^2}+\sqrt{\left(2\left(-5\right)\right)^2}\)
b. \(\dfrac{\sqrt{270}}{\sqrt{30}}-\sqrt{1,8}.\sqrt{20}\)
a, \(\sqrt{\left(3-\sqrt{2}\right)^2}+\sqrt{\left(2\left(-5\right)\right)^2}\)
\(=\left|3-\sqrt{2}\right|+\sqrt{\left(-10\right)^2}\)
\(=3-\sqrt{2}+\left|-10\right|\)
\(=3-\sqrt{2}+10\)
\(=13-\sqrt{2}\)
b, \(\dfrac{\sqrt{270}}{\sqrt{30}}-\sqrt{1,8}.\sqrt{20}\)
\(=\sqrt{9}-\sqrt{1,8.20}\)
\(=3-\sqrt{36}\)
\(=3-6\)
\(=-3\)
Thực hiện phép tính
a)\(\dfrac{\sqrt[3]{135}}{\sqrt[3]{5}}-\sqrt[3]{54}.\sqrt[3]{4}\)
b)\(\left(\sqrt[3]{25}-\sqrt[3]{10}+\sqrt[3]{4}\right)\)\(\left(\sqrt[3]{5}+\sqrt[3]{2}\right)\)
`a)\root[3]{135}/\root[3]{5}-\root[3]{54}.\root[3]{4}`
`=\root[3]{135/5}-\root[3]{54.4}`
`=\root[3]{27}-\root[3]{216}`
`=3-6=-3`
`b)(\root[3]{25}-\root[3]{10}+\root[3]{4})(\root[3]{5}+\root[3]{2})`
`=5+\root[3]{50}-\root[3]{50}-\root[3]{20}+\root[3]{20}+2`
`=7`.
thực hiện phép tính
a, \(\dfrac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
b, \(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
c, \(\sqrt{2-\sqrt{3}}.\left(\sqrt{5}+\sqrt{2}\right)\)
d, \(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
e, \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
f, \(\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}\)
g, \(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
h, \(\dfrac{6+4\sqrt{2}}{\sqrt{2}+\sqrt{6+4\sqrt{2}}}+\dfrac{6-4\sqrt{2}}{\sqrt{2}+\sqrt{6+4\sqrt{2}}}\)
i, \(\dfrac{\left(\sqrt{5+2}\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)
k, \(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
l, \(\dfrac{4}{\sqrt{3}+1}+\dfrac{1}{\sqrt{3}-2}+\dfrac{6}{\sqrt{3}-3}\)
m, \(\left(\sqrt{2}+1\right)^3-\left(\sqrt{2}-1\right)^3\)
n, \(\dfrac{\sqrt{3}}{1-\sqrt{\sqrt{3+1}}}+\dfrac{\sqrt{3}}{1+\sqrt{\sqrt{3+1}}}\)
* Thực hiện phép tính
a. \(\sqrt{\left(3-\sqrt{2}\right)^2}+\sqrt{2\left(-5\right)^2}\)
b. \(\dfrac{\sqrt{270}}{\sqrt{30}}-\sqrt{1,8}.\sqrt{20}\)
* Thực hiện phép tính
a. \(\sqrt{\left(3-\sqrt{2}\right)^2}+\sqrt{2\left(-5\right)^2}\)
b. \(\dfrac{\sqrt{270}}{\sqrt{30}}-\sqrt{1,8}.\sqrt{20}\)
Thực hiện phép tính
a) (\(2\sqrt{3}-\sqrt{2}\))2+\(2\sqrt{24}\)
b) \(\left(3\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+2\sqrt{3}\right)-\sqrt{60}\)
\(a,\left(2\sqrt{3}-\sqrt{2}\right)^2+2\sqrt{24}=\left[\left(2\sqrt{3}\right)^2-2.2.\sqrt{3}.\sqrt{2}+\left(\sqrt{2}\right)^2\right]+2\sqrt{24}\\ =\left[12-4\sqrt{6}+2\right]+2\sqrt{24}=14-4\sqrt{6}+4\sqrt{6}=14\\ b,\left(3\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+2\sqrt{3}\right)-\sqrt{60}=3\sqrt{5}.\sqrt{5}-2\sqrt{3}.\sqrt{3}+3\sqrt{5}.2\sqrt{3}-\sqrt{3}.\sqrt{5}-\sqrt{60}\\ =15-6+6\sqrt{15}-\sqrt{15}-\sqrt{2^2.15}\\ =9+3\sqrt{15}\)