rút gọn các biểu thức sau:$\dfrac{1}{2}\sqrt{20} 5$$\sqrt{16} \sqrt{64}$$\sqrt{20}-\sqrt{45} 3\sqrt{18}$$\sqrt{\left(2-\sqrt{2}\right)^2} \sqrt{2}$A= \(\dfrac{2}{\sqrt{7}-5}-\dfrac{2}{\sqrt{7}...

1

NL

Nguyễn Lê Phước Thịnh

15 tháng 7 2021

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

b1,tínha,$\sqrt{\left(\sqrt{7}-4\right)^2}+\sqrt{8-2\sqrt{7}}$b,$\sqrt{\left(\sqrt{5}-2\right)^2}+\sqrt{6+2\sqrt{5}}$b2,rút gọn các biểu thức...

W

WHAT

26 tháng 12 2023

2

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.

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

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

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

1) Rút gọn các biểu thức sau:a) $\sqrt[3]{27}$ - $\sqrt[3]{-8}$ - $\sqrt[3]{125}$b) $\sqrt{20}$ - $\sqrt{45}$ + 3$\sqrt{18}$ + $\sqrt{72}$c) 2$\sqrt{5}$ + $\sqrt{\left(1-\sqrt{5}\right)^2}$ d) $\dfrac{1}{\sqrt{3}+1}$ + $\dfrac{1}{\sqrt{3}-1}$ - 2$\sqrt{3}$e) $\dfrac{a-b}{\sqrt{a}-\sqrt{b}}$ - $\dfrac{\sqrt{a^3}-\sqrt{b^3}}{a-b}$ với a ≥ 0 , b≥0 , a ≠...

LQ

Lê Quỳnh Chi Phạm

25 tháng 12 2023

#Tiếng anh lớp 9

0

LL

Ly Ly

4 tháng 7 2021

* Rút gọn biểu thức
a. $3\sqrt{2}-4\sqrt{18}+2\sqrt{32}-\sqrt{50}$
b. $\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}+\sqrt{18}$
c. $5\sqrt{\dfrac{1}{5}}+\dfrac{1}{3}\sqrt{45}+\dfrac{5-\sqrt{5}}{\sqrt{5}}$
d. $\sqrt{7-4\sqrt{3}}+\sqrt{\left(1+\sqrt{3}\right)^2}$

2

NN

Nguyễn Ngọc Lộc

4 tháng 7 2021

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

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

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

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

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

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

$=2-\sqrt{3}+1+\sqrt{3}=2$

AT

An Thy

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

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

TB

Trần Bình An

13 tháng 7 2017

Rút gọn các biểu thức sau:

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

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

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

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

giúp nha

3

HL

Hà Linh

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

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

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

NT

Ngô Thanh Sang

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

MH

Minh harry

19 tháng 8 2021

Rút gọn các biểu thức...

2

NL

Nguyễn Lê Phước Thịnh

19 tháng 8 2021

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: $\dfrac{1}{4-3\sqrt{2}}-\dfrac{1}{4+3\sqrt{2}}$

$=\dfrac{4+3\sqrt{2}-4+3\sqrt{2}}{-2}$

$=-\dfrac{6\sqrt{2}}{2}=-3\sqrt{2}$

LL

Lấp La Lấp Lánh

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

Câu 1: Rút gọn các biểu thức sau: A= ($\sqrt{48}$ - 2$\sqrt{3}$ + 2$\sqrt{5}$ )$\sqrt{5}$ - 2$\sqrt{45}$-$\sqrt{3}$B= ($\dfrac{1}{\sqrt{5}-\sqrt{2}}$$-\dfrac{1}{\sqrt{5}+\sqrt{2}}$).$\dfrac{1}{\left(\sqrt{2}+1\right)^2}$C= $2\sqrt{a}$-$\sqrt{9a^3}$ a$^2$ $\sqrt{\dfrac{4}{a}}$+ $\dfrac{2}{a^2}$$\sqrt{25a^3}$ với a >...

6M

6.Phạm Minh Châu

2 tháng 10 2021

1

NL

Nguyễn Lê Phước Thịnh

2 tháng 10 2021

a: Ta có: $A=\left(\sqrt{48}-2\sqrt{3}+2\sqrt{5}\right)\cdot\sqrt{5}-2\sqrt{45}-\sqrt{3}$

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

$=2\sqrt{15}+10-6\sqrt{5}-\sqrt{3}$

b: Ta có: $B=\left(\dfrac{1}{\sqrt{5}-\sqrt{2}}-\dfrac{1}{\sqrt{5}+\sqrt{2}}\right)\cdot\dfrac{1}{\left(\sqrt{2}+1\right)^2}$

$=\dfrac{\sqrt{5}+\sqrt{2}-\sqrt{5}+\sqrt{2}}{3}\cdot\dfrac{1}{3+2\sqrt{2}}$

$=\dfrac{2\sqrt{2}}{9+6\sqrt{2}}=\dfrac{-8+6\sqrt{2}}{3}$

Rút gọn các biểu thức sau : a) $\sqrt{18\left(\sqrt{2}-\sqrt{3}\right)^2}$ - $\sqrt{54}$b) $\dfrac{a+\sqrt{ab}}{\sqrt{a}-\sqrt{b}}$ - a$\sqrt{\dfrac{1}{a}}$c) ( $\sqrt{28}$ -...

NA

ngọc ánh 2k8

1 tháng 8 2023

1

NL

Nguyễn Lê Phước Thịnh

1 tháng 8 2023

a: $=3\sqrt{2}\left(\sqrt{3}-\sqrt{2}\right)-3\sqrt{6}$

=3căn 6-6-3căn 6=-6

b: $=\dfrac{a+\sqrt{ab}}{\sqrt{a}-\sqrt{b}}-\sqrt{a}$

$=\dfrac{a+\sqrt{ab}-a+\sqrt{ab}}{\sqrt{a}-\sqrt{b}}=\dfrac{2\sqrt{ab}}{\sqrt{a}-\sqrt{b}}$

QE

Quynh Existn't

10 tháng 7 2021

Tính:
$A=3\sqrt{20}-\sqrt{45}+2\sqrt{18}+\sqrt{72}$
$B=\dfrac{12}{3-\sqrt{5}}-\dfrac{16}{\sqrt{5}+1}$
$C=10\sqrt{\dfrac{1}{5}}+\dfrac{1}{5}\sqrt{125}-2\sqrt{20}$
$E=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}$
$F=\sqrt{6+2\sqrt{5}}-\sqrt{9-4\sqrt{5}}$

2

NL

Nguyễn Lê Phước Thịnh

10 tháng 7 2021

a) Ta có: $A=3\sqrt{20}-\sqrt{45}+2\sqrt{18}+\sqrt{72}$

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

$=3\sqrt{5}+12\sqrt{2}$

b) Ta có: $B=\dfrac{12}{3-\sqrt{5}}-\dfrac{16}{\sqrt{5}+1}$

$=\dfrac{12\left(3+\sqrt{5}\right)}{4}-\dfrac{16\left(\sqrt{5}-1\right)}{4}$

$=3\left(3+\sqrt{5}\right)-4\left(\sqrt{5}-1\right)$

$=9+3\sqrt{5}-4\sqrt{5}+4$

$=13-\sqrt{5}$

c) Ta có: $C=10\sqrt{\dfrac{1}{5}}+\dfrac{1}{5}\sqrt{125}-2\sqrt{20}$

$=\dfrac{10}{\sqrt{5}}+\dfrac{1}{5}\cdot5\sqrt{5}-2\cdot2\sqrt{5}$

$=2\sqrt{5}+\sqrt{5}-4\sqrt{5}$

$=-\sqrt{5}$

Đúng(2)

NL

Nguyễn Lê Phước Thịnh

10 tháng 7 2021

e) Ta có: $E=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}$

$=\sqrt{3}+1-2+\sqrt{3}$

$=2\sqrt{3}-1$

f) Ta có: $F=\sqrt{6+2\sqrt{5}}-\sqrt{9-4\sqrt{5}}$

$=\sqrt{5}+1-\sqrt{5}+2$

=3

QE

Quynh Existn't

10 tháng 7 2021

Tính:

$A=3\sqrt{20}-\sqrt{45}+2\sqrt{18}+\sqrt{72}$
$B=\dfrac{12}{3-\sqrt{5}}-\dfrac{16}{\sqrt{5}+1}$

$C=10\sqrt{\dfrac{1}{5}}+\dfrac{1}{5}\sqrt{125}-2\sqrt{20}$

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

$F=\sqrt{6+2\sqrt{5}}-\sqrt{9-4\sqrt{5}}$

2

NL

Nguyễn Lê Phước Thịnh

10 tháng 7 2021

e) Ta có: $E=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}$

$=\sqrt{3}+1-2+\sqrt{3}$

$=2\sqrt{3}-1$

f) Ta có: $F=\sqrt{6+2\sqrt{5}}-\sqrt{9-4\sqrt{5}}$

$=\sqrt{5}+1-\sqrt{5}+2$

=3

Đúng(3)

NL

Nguyễn Lê Phước Thịnh

10 tháng 7 2021

a) Ta có: $A=3\sqrt{20}-\sqrt{45}+2\sqrt{18}+\sqrt{72}$

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

$=3\sqrt{5}+12\sqrt{2}$

b) Ta có: $B=\dfrac{12}{3-\sqrt{5}}-\dfrac{16}{\sqrt{5}+1}$

$=\dfrac{12\left(3+\sqrt{5}\right)}{4}-\dfrac{16\left(\sqrt{5}-1\right)}{4}$

$=3\left(3+\sqrt{5}\right)-4\left(\sqrt{5}-1\right)$

$=9+3\sqrt{5}-4\sqrt{5}+4$

$=13-\sqrt{5}$