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a: Ta có: \(2\sqrt{28}+2\sqrt{63}-3\sqrt{175}+\sqrt{112}-\sqrt{20}\)

\(=4\sqrt{7}+6\sqrt{7}-15\sqrt{7}+4\sqrt{7}-2\sqrt{5}\)

\(=-\sqrt{7}-2\sqrt{5}\)

a: \(=10\sqrt{2}-4\sqrt{2}+6\sqrt{2}=12\sqrt{2}\)

b: \(=5\sqrt{7}-4\sqrt{7}+3\sqrt{7}=4\sqrt{7}\)

c: \(=\dfrac{3}{2}\sqrt{6}+\dfrac{2}{3}\sqrt{6}-2\sqrt{6}=\dfrac{1}{6}\sqrt{6}\)

d: \(=8\sqrt{5}-15\sqrt{5}+15\sqrt{5}-3\sqrt{5}=5\sqrt{5}\)

e: \(=\sqrt{5}+\dfrac{2}{5}\sqrt{5}+\sqrt{5}=2.4\sqrt{5}\)

f: \(=\dfrac{1}{5}\sqrt{5}+\dfrac{3}{2}\sqrt{2}+\dfrac{5}{2}\sqrt{2}=\dfrac{1}{5}\sqrt{5}+4\sqrt{2}\)

30 tháng 9 2017

Rút gọn biểu thức chứa căn bậc hai

30 tháng 9 2017

Rút gọn biểu thức chứa căn bậc hai

24 tháng 9 2023

`a)2\sqrt{28}+\sqrt{63}-\sqrt{112}`

`=4\sqrt{7}+3\sqrt{7}-4\sqrt{7}`

`=3\sqrt{7}`.

`b)3\sqrt{48}-5\sqrt{108}+6\sqrt{1/3}`

`=12\sqrt{3}-30\sqrt{3}+2\sqrt{[3^2]/3}`

`=-18\sqrt{3}+2\sqrt{3}`

`=-16\sqrt{3}`.

13 tháng 7 2017

a) \(\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}\)

= \(2\sqrt{5}-3\sqrt{5}+9\sqrt{2}+6\sqrt{2}\)

= \(-\sqrt{5}+15\sqrt{2}\)

b) \(\left(\sqrt{28}-2\sqrt{3}+\sqrt{7}\right)\sqrt{7}+\sqrt{84}\)

= \(\left(2\sqrt{7}-2\sqrt{3}+\sqrt{7}\right)\sqrt{7}+2\sqrt{21}\)

= \(2.7-2\sqrt{21}+7+2\sqrt{21}=14+7=21\)

c) \(\left(\sqrt{6}+\sqrt{5}\right)^2-\sqrt{120}\)

= \(6+2\sqrt{6}.\sqrt{5}+5-2\sqrt{30}\)

= \(11+2\sqrt{30}-2\sqrt{30}=11\)

d) \(\left(\dfrac{1}{2}-\sqrt{\dfrac{1}{2}}-\dfrac{3}{2}\sqrt{2}+\dfrac{4}{5}\sqrt{200}\right):\dfrac{1}{8}\)

= \(\left(\dfrac{1}{2}-\sqrt{\dfrac{1}{2}}-\dfrac{3}{2}\sqrt{2}+8\sqrt{2}\right).8\)

= \(4-4\sqrt{2}-12\sqrt{2}+64\sqrt{2}=4+48\sqrt{2}\)

13 tháng 7 2017

Bài này dễ ẹc ( đâu có khó đâu :)) )

a) \(\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}\)

\(=\sqrt{2^2.5}-\sqrt{3^2.5}+3\sqrt{3^2.2}+\sqrt{6^2.2}\)

\(=2\sqrt{5}-3\sqrt{5}+9\sqrt{2}+6\sqrt{2}\)

\(=\left(2-3\right)\sqrt{5}+\left(9+6\right)\sqrt{2}\)

\(=15\sqrt{2}-\sqrt{5}\)

b) \(\left(\sqrt{28}-2\sqrt{3}+\sqrt{7}\right)\sqrt{7}+\sqrt{84}\)

\(=\sqrt{2^2.7}.\sqrt{7}-2\sqrt{3}.\sqrt{7}+\sqrt{7}.\sqrt{7}+\sqrt{2^2.21}\)

\(=2.7-2\sqrt{21}+7+2\sqrt{21}\)

\(=14+7+\left(2-2\right)\sqrt{21}=21\)

c) \(\left(\sqrt{6}+\sqrt{5}\right)^2-\sqrt{120}\)

\(=6+2\sqrt{30}+5-\sqrt{2^2.30}\)

\(=6+5+2\sqrt{30}-2\sqrt{30}=11\)

d) \(\left(\dfrac{1}{2}\sqrt{\dfrac{1}{2}}-\dfrac{3}{2}\sqrt{2}+\dfrac{4}{5}\sqrt{200}\right):\dfrac{1}{8}\)

\(=\left(\dfrac{1}{2}\sqrt{\dfrac{2}{2^2}}-\dfrac{3}{2}\sqrt{2}+\dfrac{4}{5}\sqrt{10^2.2}\right):\dfrac{1}{8}\)

\(=\left(\dfrac{1}{4}\sqrt{2}-\dfrac{3}{2}\sqrt{2}+8\sqrt{2}\right).8\)

\(=2\sqrt{2}-12\sqrt{2}+64\sqrt{2}=54\sqrt{2}\)

Hok tốt

16 tháng 10 2018

2]\(\sqrt{3}\)+1+\(\sqrt{4-4\sqrt{3}+3}\)=\(\sqrt{3}+1+\sqrt{\left(2-\sqrt{3}\right)^2}=\sqrt{3}+1+2-\sqrt{3}=3\)

4\(\left(\dfrac{\sqrt{3}.\left(2+\sqrt{3}\right)+2.\left(2-\sqrt{3}\right)}{\left(2-\sqrt{3}\right).\left(2+\sqrt{3}\right)}\right)=\dfrac{\sqrt{3}.\left(2+\sqrt{3}\right)+2.\left(2-\sqrt{3}\right)}{1}\)

19 tháng 10 2022

1: \(=2\sqrt{7}-12\sqrt{7}+15\sqrt{7}+27\sqrt{7}=32\sqrt{7}\)

3: \(=\sqrt{5}-2-\sqrt{14+6\sqrt{5}}\)

\(=\sqrt{5}-2-3-\sqrt{5}=-5\)

4: \(=2\sqrt{3}+3+4-2\sqrt{3}=7\)

5: \(=3-\sqrt{2}+3+\sqrt{2}+4-3=7\)

6: \(=\sqrt{\dfrac{6+2\sqrt{5}}{4}}+\sqrt{\dfrac{14-6\sqrt{5}}{4}}\)

\(=\dfrac{\sqrt{5}+1+3-\sqrt{5}}{2}=\dfrac{4}{2}=2\)

8: \(=\sqrt{5}-1+\sqrt{\dfrac{\left(3-\sqrt{5}\right)^2}{4}}-\sqrt{\dfrac{\left(3+\sqrt{5}\right)^2}{4}}\)

\(=\sqrt{5}-1+\dfrac{3-\sqrt{5}}{2}-\dfrac{3+\sqrt{5}}{2}\)

\(=\dfrac{2\sqrt{5}-2+3-\sqrt{5}-3-\sqrt{5}}{2}=\dfrac{-2}{2}=-1\)

15 tháng 7 2017

a) \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\sqrt{2}-\sqrt{5}=\sqrt{16}-6+\sqrt{20}-\sqrt{5}=4-6+2\sqrt{5}-\sqrt{5}=\sqrt{5}-2\)

b) \(0,2\sqrt{\left(-10\right)^3.3}+2\sqrt{\left(\sqrt{3}-\sqrt{5}\right)^2}=0,2\left|-10\right|\sqrt{3}+2\left|\sqrt{3}-\sqrt{5}\right|=0,2.10.\sqrt{3}+2\left(\sqrt{5}-\sqrt{3}\right)=2\sqrt{3}+2\sqrt{5}-2\sqrt{3}=2\sqrt{5}\)

c) \(\left(\dfrac{1}{2}\sqrt{\dfrac{1}{2}}-\dfrac{3}{2}\sqrt{2}+\dfrac{4}{5}\sqrt{200}\right):\dfrac{1}{8}=\left(\dfrac{1}{2}\sqrt{\dfrac{2}{4}}-\dfrac{3}{2}\sqrt{2}+8\sqrt{2}\right):\dfrac{1}{8}=\left(\dfrac{1}{4}\sqrt{2}-\dfrac{2}{3}\sqrt{2}+8\sqrt{2}\right):\dfrac{1}{8}=\dfrac{27}{4}\sqrt{2}.8=54\sqrt{2}\)

d) \(2\sqrt{\left(\sqrt{2}-3\right)^2}+\sqrt{2.\left(-3\right)^2}-5\sqrt{\left(-1\right)^4}=2\left(3-\sqrt{2}\right)+3\sqrt{2}-5=6-2\sqrt{2}+3\sqrt{2}-5=1+\sqrt{2}\)

20 tháng 6 2018

a) \(3\sqrt{8}-4\sqrt{18}+5\sqrt{32}-\sqrt{50}=3\sqrt{4.2}-4\sqrt{9.2}+5\sqrt{16.2}-\sqrt{25.2}=6\sqrt{2}-12\sqrt{2}+20\sqrt{2}-5\sqrt{2}=9\sqrt{2}\)b) \(\left(15\sqrt{50}+5\sqrt{200}-3\sqrt{450}\right):10=\left(15\sqrt{50}+5\sqrt{50.4}-3\sqrt{50.9}\right):10=\left(15\sqrt{50}+10\sqrt{50}-9\sqrt{50}\right):10=\dfrac{16\sqrt{50}}{10}=\dfrac{16\sqrt{25.2}}{10}=\dfrac{80\sqrt{2}}{10}=8\sqrt{2}\) c) \(2\sqrt{28}+2\sqrt{63}-3\sqrt{175}+\sqrt{112}=2\sqrt{7.4}+2\sqrt{7.9}-3\sqrt{7.25}+\sqrt{7.16}=4\sqrt{7}+6\sqrt{7}-15\sqrt{7}+4\sqrt{7}=-\sqrt{7}\)

d)
\(\left(\sqrt{14}-3\sqrt{2}\right)^2+6\sqrt{28}=14-2.3\sqrt{2.14}+18+6\sqrt{28}=32-6\sqrt{28}+6\sqrt{28}=32\)

23 tháng 4 2017

a, \(3\sqrt{5}\)

b, \(\dfrac{9\sqrt{2}}{2}\)

c, \(15\sqrt{2}-\sqrt{5}\)

d, \(\dfrac{17\sqrt{2}}{5}\)