thực hiện phép tính bằng cách hợp lí nhất :
a, \(\left(2\sqrt{2}-\sqrt{5}+3\sqrt{2}\right)\left(\sqrt{18}-\sqrt{20}+\sqrt{8}\right)\)
help me please !!!!!!!!!!!!!!!
thực hiện phép tính
\(\sqrt{\left(\sqrt{3}-2\right)^2}+\sqrt{\left(3-\sqrt{3}\right)^2}\)
Help me
\(\sqrt{\left(\sqrt{3}-2\right)^2}+\sqrt{\left(3-\sqrt{3}\right)^2}\)
\(=\left|\sqrt{3}-2\right|+\left|3-\sqrt{3}\right|\)
\(=2-\sqrt{3}+3-\sqrt{3}\)
\(=5-2\sqrt{3}\)
\(=\left|\sqrt{3}-2\right|+\left|3-\sqrt{3}\right|\\ =\left(2-\sqrt{3}\right)+\left(3-\sqrt{3}\right)\\ =2-\sqrt{3}+3-\sqrt{3}=5-2\sqrt{3}\)
Thực hiện các phép tính (không được ghi mỗi kết quả không, phải giải chi tiết)
A = \(2\sqrt{10}.3\sqrt{8}.2\)
B = \(\sqrt{20}\left(2\sqrt{3}-\sqrt{5}\right)\)
C = \(\left(2\sqrt{5}-3\right)\left(2\sqrt{5}+3\right)\)
a: \(=12\sqrt{80}=48\sqrt{5}\)
b: \(=2\sqrt{5}\cdot2\sqrt{3}-10=4\sqrt{15}-10\)
c: =20-9=11
Thực hiện phép tính:
\(\left(2\sqrt{2}-\sqrt{5}+3\sqrt{2}\right)\left(\sqrt{18}-\sqrt{20}+2\sqrt{2}\right)\)
\(\left(1+\sqrt{2}-\sqrt{5}\right)\left(1+\sqrt{2}+\sqrt{5}\right)\)
\(\left(2\sqrt{2}-\sqrt{5}+3\sqrt{2}\right)\left(\sqrt{18}-\sqrt{20}+2\sqrt{2}\right)\)
\(=\left(2\sqrt{2}-\sqrt{5}+3\sqrt{2}\right)\left(3\sqrt{2}-2\sqrt{5}+2\sqrt{2}\right)\)
\(=\left(5\sqrt{2}-\sqrt{5}\right)\left(5\sqrt{2}-2\sqrt{5}\right)\)
\(=50-10\sqrt{10}-5\sqrt{10}+10\)
\(=60-15\sqrt{10}\)
\(\left(1+\sqrt{2}-\sqrt{5}\right)\left(1+\sqrt{2}+\sqrt{5}\right)\)
\(=\left(1+\sqrt{2}\right)^2-5\)
\(=1+2\sqrt{2}+2-5\)
\(2\sqrt{2}-2\)
Thực hiện phép tính
\(\left(2\sqrt{8}+3\sqrt{5}-7\sqrt{2}\right)\left(\sqrt{72}-5\sqrt{20}-2\sqrt{2}\right)\)
* Thực hiện phép tính:
a. \(2\sqrt{18}-9\sqrt{50}+3\sqrt{8}\)
b. \(\left(\sqrt{7}-\sqrt{3}\right)^2+7\sqrt{84}\)
c. \(\left(\dfrac{6-2\sqrt{2}}{3-\sqrt{2}}\dfrac{5}{\sqrt{5}}\right):\dfrac{1}{2-\sqrt{5}}\)
* Tìm x, biết:
a. \(\sqrt{\left(2x+3\right)^2}=8\)
b. \(\sqrt{9x}-7\sqrt{x}=8-6\sqrt{x}\)
c. \(\sqrt{9x-9}+1=13\)
bài 1:
a: Ta có: \(2\sqrt{18}-9\sqrt{50}+3\sqrt{8}\)
\(=6\sqrt{2}-45\sqrt{2}+6\sqrt{2}\)
\(=-33\sqrt{2}\)
b: Ta có: \(\left(\sqrt{7}-\sqrt{3}\right)^2+7\sqrt{84}\)
\(=10-2\sqrt{21}+14\sqrt{21}\)
\(=12\sqrt{21}+10\)
Bài 2:
a: Ta có: \(\sqrt{\left(2x+3\right)^2}=8\)
\(\Leftrightarrow\left|2x+3\right|=8\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+3=8\\2x+3=-8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-\dfrac{11}{2}\end{matrix}\right.\)
b: Ta có: \(\sqrt{9x}-7\sqrt{x}=8-6\sqrt{x}\)
\(\Leftrightarrow4\sqrt{x}=8\)
hay x=4
c: Ta có: \(\sqrt{9x-9}+1=13\)
\(\Leftrightarrow3\sqrt{x-1}=12\)
\(\Leftrightarrow x-1=16\)
hay x=17
* Thực hiện phép tính.
a.\(2\sqrt{18}-9\sqrt{50}+3\sqrt{8}\)
b.\(\left(\sqrt{7}-\sqrt{3}\right)^2+7\sqrt{84}\)
c.\(\left(\dfrac{6-2\sqrt{2}}{3-\sqrt{2}}-\dfrac{5}{\sqrt{5}}\right).\dfrac{1}{2-\sqrt{5}}\)
d.\(\sqrt{\left(2-\sqrt{5}\right)^2-\sqrt{5}}\)
a) \(\text{2}\sqrt{\text{18}}-9\sqrt{50}+3\sqrt{8}\)
= \(\text{6}\sqrt{\text{2}}-45\sqrt{2}+6\sqrt{2}\)
= \(-33\sqrt{2}\)
b) = \(7-2.\sqrt{7}.\sqrt{3}+3+7.2\sqrt{21}\)
= \(10-2\sqrt{21}+14\sqrt{21}\)
= \(10+12\sqrt{21}\)
Thực hiện phép tính:
a) \(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
b) \(\left(1+\sqrt{2}+\sqrt{3}\right)\left(1-\sqrt{2}-\sqrt{3}\right)\)
a) Ta có: \(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
\(=\dfrac{-2\left(\sqrt{3}-\sqrt{8}\right)}{\sqrt{6}\left(\sqrt{3}-\sqrt{6}\right)}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{6}\left(\sqrt{5}+\sqrt{27}\right)}\)
\(=\dfrac{-3}{\sqrt{6}}=\dfrac{-3\sqrt{6}}{6}=\dfrac{-\sqrt{6}}{2}\)
b) Ta có: \(\left(1+\sqrt{2}+\sqrt{3}\right)\left(1-\sqrt{2}-\sqrt{3}\right)\)
\(=1-\left(\sqrt{2}+\sqrt{3}\right)^2\)
\(=1-5-2\sqrt{6}\)
\(=-4-2\sqrt{6}\)
1.thực hiện phép tính: \(\left(3\sqrt{8}-\sqrt{18}+5\sqrt{\dfrac{1}{2}}+\sqrt{50}\right).3\sqrt{2}\)
2.giải pt:\(\sqrt{4x^2-4x+1}-5=2\)
1. \(=\left(6\sqrt{2}-3\sqrt{2}+\dfrac{5\sqrt{2}}{2}+5\sqrt{2}\right).3\sqrt{2}=\left(8\sqrt{2}+\dfrac{5\sqrt{2}}{2}\right).3\sqrt{2}=8\sqrt{2}.3\sqrt{2}+\dfrac{5\sqrt{2}}{2}.3\sqrt{2}=48+15=63\)
2. \(\Leftrightarrow\left|2x-1\right|=7\\ \Leftrightarrow\left[{}\begin{matrix}2x-1=-7\\2x-1=7\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-3\\x=4\end{matrix}\right.\)
Bài 1: Thực hiện phép tính :
a,\(\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}\)
b,\(\left(\sqrt{125}+\sqrt{245}-\sqrt{5}\right):\sqrt{5}\)
c,\(\left(2\sqrt{18}-5\sqrt{32}+6\sqrt{2}\right):\sqrt{2}\)
a: Ta có: \(\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}\)
\(=6\sqrt{7}-10\sqrt{7}+12\sqrt{7}-8\sqrt{7}\)
\(=0\)
b: Ta có: \(\left(\sqrt{125}+\sqrt{245}-\sqrt{5}\right):\sqrt{5}\)
\(=5+7-1\)
=11