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AH
Akai Haruma
Giáo viên
29 tháng 12 2023

Bài 1:

a/

$\sqrt{(\sqrt{7}-4)^2}+\sqrt{8-2\sqrt{7}}$

$=|\sqrt{7}-4|+\sqrt{7+1-2\sqrt{7}}=|\sqrt{7}-4|+\sqrt{(\sqrt{7}-1)^2}$

$=4-\sqrt{7}+|\sqrt{7}-1|=4-\sqrt{7}+\sqrt{7}-1=3$

b/

\(\sqrt{(\sqrt{5}-2)^2}+\sqrt{6+2\sqrt{5}}\\ =|\sqrt{5}-2|+\sqrt{5+1+2\sqrt{5}}\\ =\sqrt{5}-2+\sqrt{(\sqrt{5}+1)^2}\\ =\sqrt{5}-2+|\sqrt{5}+1|=\sqrt{5}-2+\sqrt{5}+1=2\sqrt{5}-1\)

AH
Akai Haruma
Giáo viên
29 tháng 12 2023

Bài 2:

a. $=\sqrt{5}+\sqrt{5}+\sqrt{5}=3\sqrt{5}$

b. $=\frac{\sqrt{2}}{2}+\frac{3\sqrt{2}}{2}+\frac{5\sqrt{2}}{2}$

$=\frac{\sqrt{2}+3\sqrt{2}+5\sqrt{2}}{2}=\frac{9\sqrt{2}}{2}$

c.

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

$=-\sqrt{5}+15\sqrt{2}$
d.

$=0,1.10\sqrt{2}+2.\frac{\sqrt{2}}{5}+0,4.5\sqrt{2}$

$=\sqrt{2}+0,4\sqrt{2}+2\sqrt{2}$

$=\sqrt{2}(1+0,4+2)=3,4\sqrt{2}$

23 tháng 4 2017

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

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

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

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

TRẢ LỜI :

Để học tốt Toán 9 | Giải bài tập Toán 9

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

Để học tốt Toán 9 | Giải bài tập Toán 9

c) √20 - √45 + 3√18 + √72

= √4.5 - √9.5 + 3√9.2 + √36.2

= 2√5 - 3√5 + 9√2 + 6√2

= -√5 + 15√2

Để học tốt Toán 9 | Giải bài tập Toán 9

23 tháng 5 2021

a) 3√5                                           b) 9√2 / 2

c) -√5 + 15√2                                d)
3,4√2

 

a) \(\dfrac{1}{2}\sqrt{20}+5=\dfrac{1}{2}\cdot2\sqrt{5}+5=5+\sqrt{5}\)

b) \(\sqrt{16}+\sqrt{64}=4+8=12\)

c) \(\sqrt{20}-\sqrt{45}+3\sqrt{18}=2\sqrt{5}-3\sqrt{5}+9\sqrt{2}=9\sqrt{2}-\sqrt{5}\)

d) \(\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{2}=2-\sqrt{2}+\sqrt{2}=2\)

5 tháng 7 2017

a, \(5\sqrt{\dfrac{1}{5}}+\dfrac{1}{2}\sqrt{20}+\sqrt{5}\)

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

\(=3\sqrt{5}\)

b, \(\sqrt{\dfrac{1}{2}}+\sqrt{4,5}+\sqrt{12,5}\)

\(=\sqrt{0,5}+3\sqrt{0,5}+5\sqrt{0,5}=9\sqrt{0,5}\)

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

\(=2\sqrt{5}-3\sqrt{5}+3\sqrt{18}+2\sqrt{18}\)

\(=-\sqrt{5}+5\sqrt{18}\)

d, \(0,1.\sqrt{200}+2\sqrt{0,08}+0,4\sqrt{50}\)

\(=\sqrt{0,01.200}+0,2.\sqrt{2}+0,4.5\sqrt{2}\)

\(=\sqrt{2}+0,2\sqrt{2}+2\sqrt{2}=3,2\sqrt{2}\)

Chúc bạn học tốt!!!

4 tháng 7 2021

\(a,=3\sqrt{2}-12\sqrt{2}+8\sqrt{2}-5\sqrt{2}\)

\(=\sqrt{2}\left(3-12+8-5\right)=-6\sqrt{2}\)

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

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

\(d,=\sqrt{3-2.2\sqrt{3}+4}+\sqrt{\left(1+\sqrt{3}\right)^2}\)

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

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

4 tháng 7 2021

a) \(3\sqrt{2}-4\sqrt{18}+2\sqrt{32}-\sqrt{50}=3\sqrt{2}-4\sqrt{9.2}+2\sqrt{16.2}-\sqrt{25.2}\)

\(=3\sqrt{2}-12\sqrt{2}+8\sqrt{2}-5\sqrt{2}=-6\sqrt{2}\)

b) \(\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}+\sqrt{18}=\left|\sqrt{2}-\sqrt{3}\right|+\sqrt{9.2}=\sqrt{3}-\sqrt{2}+3\sqrt{2}\)

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

c) \(5\sqrt{\dfrac{1}{5}}+\dfrac{1}{3}\sqrt{45}+\dfrac{5-\sqrt{5}}{\sqrt{5}}=\sqrt{25.\dfrac{1}{5}}+\dfrac{1}{3}\sqrt{9.5}+\dfrac{\sqrt{5}\left(\sqrt{5}-1\right)}{\sqrt{5}}\)

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

d) \(\sqrt{7-4\sqrt{3}}+\sqrt{\left(1+\sqrt{3}\right)^2}=\sqrt{2^2-2.2.\sqrt{3}+\left(\sqrt{3}\right)^2}+\left|\sqrt{3}+1\right|\)

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

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

31 tháng 10 2021

\(a,=\sqrt{17}-4-\sqrt{17}-2=-6\\ b,=7\left(\sqrt{3}+\sqrt{2}\right)-7\sqrt{3}-6\sqrt{2}\\ =7\sqrt{3}+7\sqrt{2}-7\sqrt{3}-6\sqrt{2}=\sqrt{2}\\ c,=\dfrac{6\sqrt{5}+12-6\sqrt{5}+12}{3}+2\sqrt{2}-\dfrac{4\sqrt{7}}{7}\\ =8+2\sqrt{2}-\dfrac{4\sqrt{7}}{7}=\dfrac{56+14\sqrt{2}-4\sqrt{7}}{7}\\ d,=\left(\dfrac{\sqrt{2}}{4}-\dfrac{6\sqrt{2}}{4}+8\sqrt{2}\right):\dfrac{1}{8}=\dfrac{-5\sqrt{2}+32\sqrt{2}}{4}\cdot8=54\sqrt{2}\)

12 tháng 8 2023

a) \(\sqrt{200}-\sqrt{32}+\sqrt{72}\)

\(=\sqrt{10^2\cdot2}-\sqrt{4^2\cdot2}+\sqrt{6^2\cdot2}\)

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

\(=\left(10-4+6\right)\sqrt{2}\)

\(=12\sqrt{2}\)

b) \(4\sqrt{20}-3\sqrt{125}+5\sqrt{45}-15\sqrt{\dfrac{1}{5}}\)

\(=4\cdot2\sqrt{5}-3\cdot5\sqrt{5}+5\cdot3\sqrt{5}-3\sqrt{5}\)

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

\(=\left(8-15+15-3\right)\sqrt{5}\)

\(=5\sqrt{5}\)

c) \(\left(2\sqrt{8}+3\sqrt{5}-7\sqrt{2}\right)\left(72-5\sqrt{20}-2\sqrt{2}\right)\)

\(=\left(2\cdot2\sqrt{2}+3\sqrt{5}-7\sqrt{2}\right)\left(72-5\cdot2\sqrt{5}-2\sqrt{2}\right)\)

\(=\left(3\sqrt{5}-3\sqrt{2}\right)\left(72-10\sqrt{5}-2\sqrt{2}\right)\)

a: Ta có: \(\dfrac{8}{\left(\sqrt{5}+\sqrt{3}\right)^2}-\dfrac{8}{\left(\sqrt{5}-\sqrt{3}\right)^2}\)

\(=\dfrac{8}{8+2\sqrt{15}}-\dfrac{8}{8-2\sqrt{15}}\)

\(=\dfrac{64-16\sqrt{15}-64-16\sqrt{15}}{4}\)

\(=\dfrac{-32\sqrt{15}}{4}=-8\sqrt{15}\)

b: Ta có: \(\dfrac{1}{4-3\sqrt{2}}-\dfrac{1}{4+3\sqrt{2}}\)

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

\(=-\dfrac{6\sqrt{2}}{2}=-3\sqrt{2}\)

19 tháng 8 2021

b) \(\dfrac{1}{4-3\sqrt{2}}-\dfrac{1}{4+3\sqrt{2}}=\dfrac{4+3\sqrt{2}-4+3\sqrt{2}}{\left(4-3\sqrt{2}\right)\left(4+3\sqrt{2}\right)}=\dfrac{6\sqrt{2}}{-2}=-3\sqrt{2}\)

c) \(\left(\dfrac{\sqrt{7}+3}{\sqrt{7}-3}-\dfrac{\sqrt{7}-3}{\sqrt{7}+3}\right):\sqrt{28}=\dfrac{\left(\sqrt{7}+3\right)^2-\left(\sqrt{7}-3\right)^2}{\left(\sqrt{7}-3\right)\left(\sqrt{7}+3\right)}:\sqrt{28}=\dfrac{16+6\sqrt{7}-16+6\sqrt{7}}{7-9}=\dfrac{12\sqrt{7}}{-2}=-6\sqrt{7}\)