\(\sqrt{13+2.2\sqrt{3}}-\left(2\sqrt{3}-2018\right)\)
= \(\sqrt{\left(2\sqrt{3}\right)^2+2.2\sqrt{3}+1}-\left(2\sqrt{3}-2018\right)\)
= \(\sqrt{\left(2\sqrt{3}+1\right)^2}-\left(2\sqrt{3}-2018\right)\)
= \(2\sqrt{3}+1-2\sqrt{3}+2018=2019\)
Bài 1: Rút gọn căn bậc 2 theo hằng đẳng thức 1:
a)\(\sqrt{\left(23-15\sqrt{3}\right)^2}\)
b) \(\sqrt{\left(2-2\sqrt{3}\right)^2}\)
c) \(\sqrt{\left(15-4\sqrt{3}\right)^2}\)
d)\(\sqrt{\left(16-6\sqrt{7}\right)^2}\)
f)\(\sqrt{\left(22-8\sqrt{3}\right)^2}\)
g) \(\sqrt{\left(9-4\sqrt{2}\right)^2}\)
h) \(\sqrt{\left(13-4\sqrt{3}\right)^2}\)
i)\(\sqrt{\left(7-3\sqrt{3}\right)^2}\)
(mink đag cần gấp)
tính
1.\(\left(\sqrt{15}-2\sqrt{3}\right)^2+12\sqrt{5}\)
2.\(3\sqrt{2}\left(4-\sqrt{2}\right)+3\left(1-2\sqrt{2}\right)^2\)
3.\(\dfrac{1}{2}\left(\sqrt{6}+\sqrt{5}\right)^2-\dfrac{1}{4}\sqrt{120}-\sqrt{\dfrac{15}{2}}\)
4.\(\left(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\right)^2\)
5.\(\left(\sqrt{\sqrt{14}+\sqrt{5}}+\sqrt{\sqrt{14}-\sqrt{5}}\right)^2\)
6.\(\left(\sqrt{3}+1\right)^3-\left(\sqrt{3}-1\right)^3\)
7.\(\left(\sqrt{2}+1\right)^3-\left(\sqrt{2}-1\right)^3\)
8.\(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)
9.\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
cho x=\(\dfrac{1}{2}\)\(\sqrt{\dfrac{\sqrt{2-1}}{\sqrt{2+1}}}\)
tính f(x)= (\(4x^5+4x^4-x^3+1\))19+\(\sqrt{\left(4x^5+4x^4-5x^3+5x+3\right)^3}\)+\(\left(\dfrac{1-\sqrt{2}}{\sqrt{2x^2}+2x}\right)^{2018}\)
a,\(\left(4\sqrt{3}+2\sqrt{5}\right)\sqrt{3}-\sqrt{60}\)
b,\(\sqrt{\left(\sqrt{3}+\sqrt{5}\right)^2}-\sqrt{\left(\sqrt{3}-\sqrt{5}\right)^2}\)
Rút gọn :
1, \(\sqrt{8}-3\sqrt{32}+\sqrt{72}\)
2, \(6\sqrt{12}-\sqrt{20}-2\sqrt{27}+\sqrt{125}\)
3 , \(3\sqrt{112}-7\sqrt{216}+4\sqrt{54}-2\sqrt{252}-3\sqrt{96}\)
4, \(3\sqrt{3}\left(3+2\sqrt{6}-\sqrt{33}\right)\)
6, \(\sqrt{2}\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)
7, \((5\sqrt{6}-4\sqrt{10}+7\sqrt{30}):\sqrt{2}\)
8, \(\left(2\sqrt{28}-3\sqrt{7}+5\sqrt{63}\right)\sqrt{112}\)
9, \(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
10, \(\left(4\sqrt{27}-2\sqrt{48}-5\sqrt{75}\right):2\sqrt{3}\)
11, \(\left(1+\sqrt{3}-\sqrt{2}\right).\left(1+\sqrt{3}+\sqrt{2}\right)\)
các bạn ơi ! giúp mik với đi !
Rút gọn biểu thức
1)\(\sqrt{2-\sqrt{3}}\) nhân \(\left(\sqrt{6}+\sqrt{2}\right)\) nhân \(\left(2+\sqrt{3}\right)\)
2)\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
3)\(\left(\sqrt{9-2\sqrt{14}}+\dfrac{5}{\sqrt{7}-\sqrt{2}}\right)^2\)
Bài 1 : rút gọn
a, \(\sqrt{8}-3\sqrt{32}+\sqrt{72}\)
b, \(6\sqrt{12}-\sqrt{20}-2\sqrt{27}+\sqrt{125}\)
c, \(3\sqrt{112}-7\sqrt{216}+4\sqrt{54}-2\sqrt{252}-3\sqrt{96}\)
bài 2 : rút gọn
1, \(3\sqrt{3}\left(3+2\sqrt{6}-\sqrt{33}\right)\)
2, \(\sqrt{2}\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)
3, \(\left(2\sqrt{2}-3\sqrt{7}+5\sqrt{63}\right)\sqrt{112}\)
4, \((5\sqrt{6}-4\sqrt{10}+7\sqrt{30}):\sqrt{2}\)
5, \(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
6, \(\left(4\sqrt{27}-2\sqrt{48}-5\sqrt{75}\right):2\sqrt{3}\)
7, \(\left(1+\sqrt{3}-\sqrt{2}\right).\left(1+\sqrt{3}+\sqrt{2}\right)\)
các bạn ơi ! giúp mik vs đi !!!!!!!!!!!!!!
CM các đẳng thức sau:
a) \(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}=9\)
b) \(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}=\sqrt{6}\)
c) \(\sqrt{\dfrac{4}{\left(2-\sqrt{5}\right)^2}}-\sqrt{\dfrac{4}{\left(2+\sqrt{5}\right)^2}}=8\)
rút gon biểu thức:
1, \(\left(\dfrac{\sqrt{1+a}}{\sqrt{1+a}-\sqrt{1-a}}+\dfrac{1-a}{\sqrt{1-a^2}-1+a}\right)\left(\sqrt{\dfrac{1}{a^2}-1}-\dfrac{1}{a}\right)\)
2, \(\dfrac{1+2019\sqrt{2018}-2018\sqrt{2019}}{\sqrt{2018}+\sqrt{2019}+\sqrt{2018.2019}}\)