câu 1 . thực hiện phép tính a. \(\sqrt{4,9.360}\) b. \(\sqrt{2,25.0,04}\) c. \(\sqrt{3\dfrac{1}{16}.2\dfrac{14}{15}}\) d. \(\sqrt{9-\sqrt{17}}-\sqrt{9 \sqrt{17}}\) e. \(\sqrt{\dfrac{144}{169}}\)...

1

PT

Phạm Thị Ngọc Huyền

30 tháng 7 2018

\(a,\sqrt{4,9.360}=\sqrt{49.36}=\sqrt{49}.\sqrt{36}=7.6=42\)

b,\(\sqrt{2,25.0,04}=\sqrt{0.09}=0.3\)

c, \(\sqrt{3\dfrac{1}{16}.2\dfrac{4}{15}}=\sqrt{\dfrac{49}{16}.\dfrac{44}{15}}=\sqrt{\dfrac{49}{16}}.\sqrt{\dfrac{44}{15}}=\dfrac{7}{4}.1,7=2,99\approx3\)

e, \(\sqrt{\dfrac{144}{169}}=\dfrac{\sqrt{144}}{\sqrt{169}}=\dfrac{12}{13}\)

g,\(\dfrac{\sqrt{27}}{\sqrt{3}}=\sqrt{\dfrac{27}{3}}=\sqrt{9}=3\)

f,\(\sqrt{2,25}=\dfrac{3}{2}\)

n,\(\sqrt{\dfrac{25}{529}}=\dfrac{\sqrt{25}}{\sqrt{529}}=\dfrac{5}{23}\)

TN

Trang Nguyễn

24 tháng 8 2021

1) thực hiện phép tính

a) \(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)

b) \(\left(6\sqrt{\dfrac{8}{9}}-5\sqrt{\dfrac{32}{25}}+14\sqrt{\dfrac{18}{49}}\right).\sqrt{\dfrac{1}{2}}\)

c) \(\sqrt{\left(\sqrt{2}-2\right)^2}-\sqrt{6+4\sqrt{2}}\)

giúp mk vs ạ mk đang cần gấp

1

LT

Lê Thị Thục Hiền

24 tháng 8 2021

a)\(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)

\(=2.\sqrt{\dfrac{4^2}{3}}-3.\sqrt{\dfrac{1}{3.3^2}}-6\sqrt{\dfrac{2^2}{3.5^2}}\)

\(=2.\dfrac{4}{\sqrt{3}}-3.\dfrac{1}{3\sqrt{3}}-6.\dfrac{2}{5\sqrt{3}}=\dfrac{8}{\sqrt{3}}-\dfrac{1}{\sqrt{3}}-\dfrac{12}{5\sqrt{3}}\)\(=\dfrac{23}{5\sqrt{3}}=\dfrac{23\sqrt{3}}{15}\)

b)\(\left(6\sqrt{\dfrac{8}{9}}-5\sqrt{\dfrac{32}{25}}+14\sqrt{\dfrac{18}{49}}\right).\sqrt{\dfrac{1}{2}}\)

\(=6\sqrt{\dfrac{8}{9}.\dfrac{1}{2}}-5\sqrt{\dfrac{32}{25}.\dfrac{1}{2}}+14\sqrt{\dfrac{18}{49}.\dfrac{1}{2}}\)

\(=6\sqrt{\dfrac{4}{9}}-5\sqrt{\dfrac{16}{25}}+14\sqrt{\dfrac{9}{49}}\)\(=6.\dfrac{2}{3}-5.\dfrac{4}{5}+14.\dfrac{3}{7}=6\)

c)\(\sqrt{\left(\sqrt{2}-2\right)^2}-\sqrt{6+4\sqrt{2}}=\left|\sqrt{2}-2\right|-\sqrt{4+2.2\sqrt{2}+2}=2-\sqrt{2}-\sqrt{\left(2+\sqrt{2}\right)^2}\)

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

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M

Moon

27 tháng 10 2023

thực hiện phép tính:

A=\(\sqrt{9}-3\sqrt{\dfrac{50}{9}}+3\sqrt{8}-\sqrt[3]{27}\)

B=\(\sqrt{\left(2-\sqrt{3}\right)^2}+\dfrac{2}{\sqrt{3}-1}-6\sqrt{\dfrac{16}{3}}\)

B1: thực hiện phép tínha )\(\dfrac{\sqrt{6}-\sqrt{15}}{\sqrt{35}-\sqrt{14}}\)b ) \(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{1-\sqrt{5}}\)c )\(\dfrac{\sqrt{3-\sqrt{5}.}\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)d ) \(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2+\sqrt{3}}}\)B2:chúng minh vế phải bằng vế...

2

NL

Nguyễn Lê Phước Thịnh

27 tháng 10 2023

A: \(A=\sqrt{9}-3\sqrt{\dfrac{50}{9}}+3\sqrt{8}-\sqrt[3]{27}\)

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

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

b: \(B=\sqrt{\left(2-\sqrt{3}\right)^2}+\dfrac{2}{\sqrt{3}-1}-6\cdot\sqrt{\dfrac{16}{3}}\)

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

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

\(=3-4\sqrt{3}\)

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H

⭐Hannie⭐

27 tháng 10 2023

\(A=\sqrt{9}-3\sqrt{\dfrac{50}{9}}+3\sqrt{8}-\sqrt[3]{27}\\ =3-3\cdot\dfrac{1}{3}\sqrt{25\cdot2}+3\sqrt{4\cdot2}-3\\ =3-1\cdot5\sqrt{2}+3\cdot2\sqrt{2}-3\\ =3-5\sqrt{2}+6\sqrt{2}-3\\ =\sqrt{2}\)

\(B=\sqrt{\left(2-\sqrt{3}\right)^2}+\dfrac{2}{\sqrt{3}-1}-6\sqrt{\dfrac{16}{3}}\\ =\left|2-\sqrt{3}\right|+\dfrac{2\left(\sqrt{3}+1\right)}{3-1}-6\cdot\dfrac{4\sqrt{3}}{3}\\ =2-\sqrt{3}+\sqrt{3}+1-8\sqrt{3}\\ =3-8\sqrt{3}\)

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N

ngọc

1 tháng 8 2021

0

DT

Dương Thị Ngọc Hân

25 tháng 7 2018

Bài 1 : Rút gọn

a) \(\dfrac{2\sqrt{3}+2}{4\sqrt{3}+4}\) b) \(\dfrac{\sqrt{10}+\sqrt{15}}{\sqrt{8}+\sqrt{12}}\) c) \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\) d) \(\sqrt{9+\sqrt{17}}\). \(\sqrt{9-\sqrt{17}}\)

3

TN

Thúy Nga

21 tháng 8 2018

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

b) \(\dfrac{\sqrt{10}+\sqrt{15}}{\sqrt{8}+\sqrt{12}}=\dfrac{\sqrt{5}\left(\sqrt{2}+\sqrt{3}\right)}{\sqrt{4}\left(\sqrt{2}+\sqrt{3}\right)}=\dfrac{\sqrt{5}}{2}\)

c) \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{4}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\ =\dfrac{\left(1+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}=1+\sqrt{2}\)

d) \(\sqrt{9+\sqrt{17}}.\sqrt{9-\sqrt{17}}=\sqrt{\left(9+\sqrt{17}\right)\left(9-\sqrt{17}\right)}\\ =\sqrt{81-17}=\sqrt{64}=8\)

PK

Phùng Khánh Linh

21 tháng 8 2018

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

\(b.\dfrac{\sqrt{10}+\sqrt{15}}{\sqrt{8}+\sqrt{12}}=\dfrac{\sqrt{5}\left(\sqrt{2}+\sqrt{3}\right)}{2\left(\sqrt{2}+\sqrt{3}\right)}=\dfrac{\sqrt{5}}{2}\)

\(c.\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\dfrac{\sqrt{2}+\sqrt{3}+2+2+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+2}=\dfrac{\sqrt{2}+\sqrt{3}+2}{\sqrt{2}+\sqrt{3}+2}+\dfrac{\sqrt{2}\left(\sqrt{2}+\sqrt{3}+2\right)}{\sqrt{2}+\sqrt{3}+2}=1+\sqrt{2}\)

\(d.\sqrt{9+\sqrt{17}}.\sqrt{9-\sqrt{17}}=\sqrt{\left(9+\sqrt{17}\right)\left(9-\sqrt{17}\right)}=\sqrt{81-17}=8\)

N

nngoc

27 tháng 7 2021

THỰC HIỆN PHÉP TÍNH

1,\(\sqrt{1\dfrac{9}{16}}\)

2,\(\dfrac{\sqrt{12,5}}{0,5}\)

3,\(\sqrt{\dfrac{25}{64}}\)

4,\(\dfrac{\sqrt{230}}{\sqrt{2,3}}\)

5,\((\sqrt{\dfrac{2}{3}}+\sqrt{\dfrac{50}{3}}-\sqrt{24}).\sqrt{6}\)

1

NL

Nguyễn Lê Phước Thịnh

27 tháng 7 2021

1) \(\sqrt{1\dfrac{9}{16}}=\sqrt{\dfrac{25}{16}}=\dfrac{5}{4}\)

2) \(\dfrac{\sqrt{12.5}}{0.5}=\sqrt{\dfrac{12.5}{0.25}}=5\sqrt{2}\)

3) \(\sqrt{\dfrac{25}{64}}=\dfrac{5}{8}\)

4) \(\dfrac{\sqrt{230}}{\sqrt{2.3}}=\sqrt{\dfrac{230}{2.3}}=\sqrt{100}=10\)

5) \(\left(\sqrt{\dfrac{2}{3}}+\sqrt{\dfrac{50}{3}}-\sqrt{24}\right)\cdot\sqrt{6}\)

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

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

\(=0\cdot\sqrt{6}=0\)

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JP

James Pham

11 tháng 8 2021

So...

1

NL

Nguyễn Lê Phước Thịnh

11 tháng 8 2021

a: \(4\sqrt{7}=\sqrt{4^2\cdot7}=\sqrt{112}\)

\(3\sqrt{13}=\sqrt{3^2\cdot13}=\sqrt{117}\)

mà 112<117

nên \(4\sqrt{7}< 3\sqrt{13}\)

b: \(3\sqrt{12}=\sqrt{3^2\cdot12}=\sqrt{108}\)

\(2\sqrt{16}=\sqrt{16\cdot2^2}=\sqrt{64}\)

mà 108>64

nên \(3\sqrt{12}>2\sqrt{16}\)

c: \(\dfrac{1}{4}\sqrt{84}=\sqrt{\dfrac{1}{16}\cdot84}=\sqrt{\dfrac{21}{4}}\)

\(6\sqrt{\dfrac{1}{7}}=\sqrt{36\cdot\dfrac{1}{7}}=\sqrt{\dfrac{36}{7}}\)

mà \(\dfrac{21}{4}>\dfrac{36}{7}\)

nên \(\dfrac{1}{4}\sqrt{84}>6\sqrt{\dfrac{1}{7}}\)

d: \(3\sqrt{12}=\sqrt{3^2\cdot12}=\sqrt{108}\)

\(2\sqrt{16}=\sqrt{16\cdot2^2}=\sqrt{64}\)

mà 108>64

nên \(3\sqrt{12}>2\sqrt{16}\)

bài 1: tính a) \(\sqrt{1,2\cdot27}\) b) \(\sqrt{55\cdot77\cdot35}\) c) (\(\sqrt{3}-\sqrt{2}\) )\(^2\) d) (3\(\sqrt{2}-1\))*(3\(\sqrt{2}+1\)) e) (\(\sqrt{6}+7\)) (\(\sqrt{3}-\sqrt{2}\)) i) \(\sqrt{\dfrac{1}{8}}\cdot\sqrt{2}\cdot\sqrt{125}\cdot\sqrt{\dfrac{1}{5}}\) h) \(\sqrt{\sqrt{2}-1}\cdot\sqrt{\sqrt{2}}+1\) bài 2: tính a) \(\sqrt{9}-\sqrt{17}\cdot\sqrt{9}+\sqrt{17}\) b) 2\(\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}\) c)...

AN

An Nhi

2 tháng 6 2018

1

NL

Nguyễn Lê Phước Thịnh

9 tháng 7 2022

Bài 1:

a: \(=\sqrt{32.4}=\dfrac{9}{5}\sqrt{10}\)

b: \(=\sqrt{5\cdot5\cdot7\cdot7\cdot11\cdot11}=5\cdot7\cdot11=385\)

c: \(=5-2\sqrt{6}\)

d: \(=18-1=17\)

e: \(=3\sqrt{2}-2\sqrt{3}+7\sqrt{3}-7\sqrt{2}=-4\sqrt{2}+5\sqrt{3}\)

Thực hiện phép tính:a) (\(\dfrac{6}{\sqrt{3}}\) - 2\(\sqrt{48}\)) (\(\sqrt{3}\) - 1)b) \(\dfrac{\left(\sqrt{5}-1\right)^2}{\sqrt{5}-3}\) - \(\sqrt{9-4\sqrt{5}}\)c) 3\(\sqrt{2a}\) - \(\sqrt{18a^3}\) + 4\(\sqrt{\dfrac{a}{2}}\) - \(\dfrac{1}{4}\)\(\sqrt{128a}\) với...

HP

Ha Pham

3 tháng 8 2023

1

NL

Nguyễn Lê Phước Thịnh

3 tháng 8 2023

a: =(2căn 3-8căn 3)(căn 3-1)

=-6căn 3*(căn 3-1)

=-18+6căn 3

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

=-2-căn 5+2=-căn 5

c: \(=3\sqrt{2a}-3a\sqrt{2a}+2\sqrt{2a}-\dfrac{1}{4}\cdot8\sqrt{2a}\)

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

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HM

Hoang Minh

22 tháng 6 2023

e,\(\sqrt{\dfrac{9}{169}}\)

f,\(\sqrt{1\dfrac{9}{16}}\)

g,\(\dfrac{\sqrt{2300}}{\sqrt{23}}\)

h,\(\dfrac{\sqrt{12,5}}{\sqrt{0,5}}\)

2

TT

Thư Thư

22 tháng 6 2023

\(e,\sqrt{\dfrac{9}{169}}=\dfrac{\sqrt{9}}{\sqrt{169}}=\dfrac{\sqrt{3^2}}{\sqrt{13^2}}=\dfrac{3}{13}\)

\(f,\sqrt{1\dfrac{9}{16}}=\sqrt{\dfrac{25}{16}}=\dfrac{\sqrt{25}}{\sqrt{16}}=\dfrac{\sqrt{5^2}}{\sqrt{4^2}}=\dfrac{5}{4}\)

\(g,\dfrac{\sqrt{2300}}{\sqrt{23}}=\sqrt{\dfrac{2300}{23}}=\sqrt{100}=\sqrt{10^2}=10\)

\(h,\dfrac{\sqrt{12,5}}{\sqrt{0,5}}=\sqrt{\dfrac{12,5}{0,5}}=\sqrt{25}=\sqrt{5^2}=5\)

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H9

HT.Phong (9A5)

22 tháng 6 2023

e, \(\sqrt{\dfrac{9}{169}}\)

\(=\sqrt{\dfrac{3^2}{13^2}}\)

\(=\dfrac{3}{13}\)

f, \(\sqrt{1\dfrac{9}{16}}\)

\(=\sqrt{\dfrac{25}{16}}\)

\(=\sqrt{\dfrac{5^2}{4^2}}\)

\(=\dfrac{5}{4}\)

g, \(\dfrac{\sqrt{2300}}{\sqrt{23}}\)

\(=\dfrac{10\sqrt{23}}{\sqrt{23}}\)

\(=10\)

h, \(\dfrac{\sqrt{12,5}}{\sqrt{0,5}}\)

\(=\dfrac{\dfrac{5\sqrt{2}}{2}}{\dfrac{\sqrt{2}}{2}}\)

\(=\dfrac{\dfrac{5\sqrt{2}}{2}\cdot2}{\sqrt{2}}\)

\(=\dfrac{5\sqrt{2}}{\sqrt{2}}=5\)