\(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}\)

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AH
Akai Haruma
Giáo viên
19 tháng 8 2022

Lời giải:

\(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}=\sqrt{3+45-2\sqrt{3.45}}-\sqrt{45}+\sqrt{18}\)

\(=\sqrt{(\sqrt{45}-\sqrt{3})^2}-\sqrt{45}+\sqrt{18}=\sqrt{45}-\sqrt{3}-\sqrt{45}+\sqrt{18}=\sqrt{18}-\sqrt{3}\)

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

15 tháng 10 2020

\(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}\)

\(=\sqrt{\left(\sqrt{45}\right)^2+\left(\sqrt{3}\right)^2-2\cdot\sqrt{45}\cdot\sqrt{3}}-\sqrt{45}+\sqrt{18}\)

\(=\sqrt{\left(\sqrt{45}-\sqrt{3}\right)^2}-\sqrt{45}+\sqrt{18}\)

\(=\left|\sqrt{45}-\sqrt{3}\right|-\sqrt{45}+3\sqrt{2}\)

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

21 tháng 12 2018

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

b) \(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}=\sqrt{48-2\sqrt{9.15}}-\sqrt{9.5}+\sqrt{9.2}=\sqrt{48-6\sqrt{15}}-3\sqrt{5}+3\sqrt{2}=\sqrt{3-2.\sqrt{3}.3\sqrt{5}+45}-3\sqrt{5}+3\sqrt{2}=\sqrt{\left(\sqrt{3}\right)^2-2.\sqrt{3}.3\sqrt{5}+\left(3\sqrt{5}\right)^2}-3\sqrt{5}+3\sqrt{2}=\sqrt{\left(\sqrt{3}-3\sqrt{5}\right)^2}-3\sqrt{5}+3\sqrt{2}=\left|\sqrt{3}-3\sqrt{5}\right|-3\sqrt{5}+3\sqrt{2}=3\sqrt{5}-\sqrt{3}-3\sqrt{5}+3\sqrt{2}=3\sqrt{2}-\sqrt{3}\)

10 tháng 7 2017

\(A=\sqrt{45-2\sqrt{135}+3}-3\sqrt{5}+3\sqrt{2}\\ =\sqrt{\left(3\sqrt{5}-\sqrt{3}\right)^2}-3\sqrt{5}+3\sqrt{2}\\ =3\sqrt{5}-\sqrt{3}-3\sqrt{5}+3\sqrt{2}\\ =3\sqrt{2}-\sqrt{3}\)

10 tháng 7 2017

\(B=\dfrac{\sqrt{5}.\sqrt{2}\left(\sqrt{5}-\sqrt{2}\right)}{\sqrt{5}-\sqrt{2}}-\dfrac{6\left(2+\sqrt{10}\right)}{10-4}-2\sqrt{10}\\ =\sqrt{10}-\dfrac{12+6\sqrt{10}}{6}-2\sqrt{10}\\ =\sqrt{10}-2-\sqrt{10}-2\sqrt{10}\\ =-2-2\sqrt{10}\)

16 tháng 12 2022

a: \(=\sqrt{5}-3\sqrt{5}-4\sqrt{3}+15\sqrt{3}=-2\sqrt{5}+11\sqrt{3}\)

b: \(=3\sqrt{10}-\sqrt{5}+6-\sqrt{2}\)

c; \(=15\sqrt{2}-10\sqrt{3}-12\sqrt{2}-\sqrt{3}=-11\sqrt{3}+3\sqrt{2}\)

d: \(=3-\sqrt{3}+\sqrt{3}-1=2\)

f: \(=\sqrt{10}-\sqrt{10}-2-2\sqrt{10}=-2-2\sqrt{10}\)

Bài 2:

a: \(=\sqrt{5}-2\)

b: \(=2\sqrt{3}+4\sqrt{3}-5\sqrt{3}-9\sqrt{3}=-8\sqrt{3}\)

c: \(=\sqrt{4+2\sqrt{2}}\cdot\sqrt{4-2\sqrt{2}}=\sqrt{16-8}=2\sqrt{2}\)

d: \(=\sqrt{2}+1-2+\sqrt{2}=2\sqrt{2}-1\)

e: \(=\dfrac{8-2\sqrt{15}+8+2\sqrt{15}}{2}-\dfrac{6+2\sqrt{5}}{4}\)

\(=\dfrac{16-3-\sqrt{5}}{2}=\dfrac{13-\sqrt{5}}{2}\)

f: \(=\sqrt{5\sqrt{3+5\sqrt{48-10\left(2+\sqrt{3}\right)}}}\)

\(=\sqrt{5\sqrt{3+5\sqrt{28-10\sqrt{3}}}}\)

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

\(=\sqrt{5\sqrt{3+25-5\sqrt{3}}}\)

\(=\sqrt{5\sqrt{28-5\sqrt{3}}}\)

Ta có: \(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}\)

\(=\sqrt{45-2\cdot\sqrt{45}\cdot\sqrt{3}+3}-\sqrt{45}+\sqrt{18}\)

\(=\sqrt{\left(\sqrt{45}-\sqrt{3}\right)^2}-\sqrt{45}+\sqrt{18}\)

\(=\sqrt{45}-\sqrt{3}-\sqrt{45}+\sqrt{18}\)

\(=\sqrt{18}-\sqrt{3}\)

Bài 1:

a) Sửa đề: \(\left(\sqrt{12}+3\sqrt{5}-4\sqrt{135}\right)\cdot\sqrt{3}\)

Ta có: \(\left(\sqrt{12}+3\sqrt{5}-4\sqrt{135}\right)\cdot\sqrt{3}\)

\(=\sqrt{12}\cdot\sqrt{3}+3\sqrt{5}\cdot\sqrt{3}-4\sqrt{135}\cdot\sqrt{3}\)

\(=6+3\sqrt{15}-36\sqrt{5}\)

b) Ta có: \(\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}\)

\(=3\sqrt{28}-5\sqrt{28}+3\sqrt{112}-2\sqrt{112}\)

\(=-2\sqrt{28}+\sqrt{112}=-\sqrt{112}+\sqrt{112}=0\)

c) Ta có: \(2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}\)

\(=2\cdot4\cdot\sqrt{5}\cdot\sqrt{\sqrt{3}}-2\cdot\sqrt{5}\cdot\sqrt{\sqrt{3}}-3\cdot2\cdot\sqrt{5}\cdot\sqrt{\sqrt{3}}\)

\(=8\sqrt{5}\cdot\sqrt{\sqrt{3}}-2\sqrt{5}\sqrt{\sqrt{3}}-6\sqrt{5}\sqrt{\sqrt{3}}\)

=0

Bài 2:

a) Ta có: \(A=\frac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\)

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

\(=\frac{1}{\sqrt{2}}\)

b) Ta có: \(B=\frac{9\sqrt{5}+3\sqrt{27}}{\sqrt{5}+\sqrt{3}}\)

\(=\frac{\sqrt{405}+\sqrt{243}}{\sqrt{5}+\sqrt{3}}\)

\(=\frac{9\left(\sqrt{5}+\sqrt{3}\right)}{\sqrt{5}+\sqrt{3}}=9\)

c) Ta có: \(C=\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)

\(=\frac{\sqrt{72}-\sqrt{48}+\sqrt{20}}{\sqrt{162}-\sqrt{108}+\sqrt{45}}\)

\(=\frac{2\left(\sqrt{18}-\sqrt{12}+\sqrt{5}\right)}{3\left(\sqrt{18}-\sqrt{12}+\sqrt{5}\right)}=\frac{2}{3}\)

19 tháng 4 2020

\(\sqrt{48-2.3\sqrt{5}.\sqrt{3}}-\sqrt{45}+\sqrt{18}=\sqrt{\left(3\sqrt{5}-\sqrt{3}\right)^2}-3\sqrt{5}+3\sqrt{2}\)

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

học tốt

8 tháng 7 2019

1,

\(2\sqrt{5}-\sqrt{125}-\sqrt{80}\\ =2\sqrt{5}-\sqrt{25\cdot5}-\sqrt{16\cdot5}\\ =2\sqrt{5}-5\sqrt{5}-4\sqrt{5}\\ =-7\sqrt{5}\)

2,

\(3\sqrt{2}-\sqrt{8}+\sqrt{50}-4\sqrt{32}\\ =3\sqrt{2}-\sqrt{4\cdot2}+\sqrt{25\cdot2}-4\sqrt{16\cdot2}\\ =3\sqrt{2}-2\sqrt{2}+5\sqrt{2}-16\sqrt{2}\\=-10\sqrt{2}\)

3,

\(\sqrt{18}-3\sqrt{80}-2\sqrt{50}+2\sqrt{45}\\ =\sqrt{9\cdot2}-3\sqrt{16\cdot5}-2\sqrt{25\cdot2}+2\sqrt{9\cdot5}\\ =3\sqrt{2}-12\sqrt{5}-10\sqrt{2}+6\sqrt{5}\\ =-7\sqrt{2}-6\sqrt{5}\)

4,

\(\sqrt{27}-2\sqrt{3}+2\sqrt{48}-3\sqrt{75}\\ =\sqrt{9\cdot3}-2\sqrt{3}+2\sqrt{16\cdot3}-3\sqrt{25\cdot2}\\ =3\sqrt{3}-2\sqrt{3}+8\sqrt{3}-15\sqrt{3}\\ =-6\sqrt{3}\)

5,

\(3\sqrt{2}-4\sqrt{18}+\sqrt{32}-\sqrt{50}\\ =3\sqrt{2}-4\sqrt{9\cdot2}+\sqrt{16\cdot2}-\sqrt{25\cdot2}\\ =3\sqrt{2}-12\sqrt{2}+4\sqrt{2}-5\sqrt{2}\\ =-10\sqrt{2}\)

8 tháng 7 2019

6,

\(2\sqrt{3}-\sqrt{75}+2\sqrt{12}-\sqrt{147}\\ =2\sqrt{3}-\sqrt{25\cdot3}+2\sqrt{4\cdot3}-\sqrt{49\cdot3}\\ =2\sqrt{3}-5\sqrt{3}+4\sqrt{3}-7\sqrt{3}\\ =-6\sqrt{3}\)

7,

\(\sqrt{20}-2\sqrt{45}-3\sqrt{80}+\sqrt{125}\\ =\sqrt{4\cdot5}-2\sqrt{9\cdot5}-3\sqrt{16\cdot5}+\sqrt{25\cdot5}\\ =2\sqrt{5}-6\sqrt{5}-12\sqrt{5}+5\sqrt{5}\\ =-11\sqrt{5}\)

8,

\(6\sqrt{12}-\sqrt{20}-2\sqrt{27}+\sqrt{125}\\ =6\sqrt{4\cdot3}-\sqrt{4\cdot5}-2\sqrt{9\cdot3}+\sqrt{25\cdot5}\\ =12\sqrt{3}-2\sqrt{5}-6\sqrt{3}+5\sqrt{5}\\ =6\sqrt{3}+3\sqrt{5}\\ =3\left(2\sqrt{3}+\sqrt{5}\right)\)

9,

\(4\sqrt{24}-2\sqrt{54}+3\sqrt{6}-\sqrt{150}\\ =4\sqrt{4\cdot6}-2\sqrt{9\cdot6}+3\sqrt{6}-\sqrt{25\cdot6}\\ =8\sqrt{6}-6\sqrt{6}+3\sqrt{6}-5\sqrt{6}=0\)

10,

\(2\sqrt{18}-3\sqrt{80}-5\sqrt{147}+5\sqrt{245}-3\sqrt{98}\\ =2\sqrt{9\cdot2}-3\sqrt{16\cdot5}-5\sqrt{49\cdot3}+5\sqrt{49\cdot5}-3\sqrt{49\cdot2}\\ =6\sqrt{2}-12\sqrt{5}-35\sqrt{3}+35\sqrt{5}-21\sqrt{2}\\ =-15\sqrt{2}-35\sqrt{3}+23\sqrt{5}\)