Giải:
#Học tốt!!!
a) 7 /24
b) 1, 08
c) 17/2
d) 15 /29
a) \(\sqrt{1\dfrac{9}{16}.5\dfrac{4}{9}.0,01}=\sqrt{\dfrac{25}{16}.\dfrac{49}{9}.0,01}=\dfrac{5}{4}.\dfrac{7}{3}.0,1=\dfrac{7}{24}\)
b) \(\sqrt{1,44.1,21-1,44.0,4}=\sqrt{1,44.\left(1,21-0,4\right)}=\sqrt{1,44.0,81}=1,2.0,9=1,08\)
c) \(\sqrt{\dfrac{165^2-124^2}{164}}=\sqrt{\dfrac{\left(165-124\right)\left(165+124\right)}{164}}=\sqrt{\dfrac{41.289}{164}}=\sqrt{\dfrac{289}{4}}=\dfrac{17}{2}\)
d) \(\sqrt{\dfrac{149^2-76^2}{457^2-384^2}}=\sqrt{\dfrac{\left(149-76\right)\left(149+76\right)}{\left(457-384\right)\left(457+384\right)}}=\sqrt{\dfrac{73.225}{73.841}}=\sqrt{\dfrac{225}{841}}=\dfrac{15}{29}\)
\(a=\dfrac{7}{24};b=1.08;\dfrac{17}{2};\dfrac{15}{29}\)
a\(\dfrac{7}{24}\)
b 1,08
c 17/2
d 15/29
a, \(\sqrt{1\dfrac{9}{16}.5\dfrac{4}{9}.0,01}=\sqrt{\dfrac{25}{16}.\dfrac{49}{9}.\dfrac{1}{100}}=\sqrt{\dfrac{25}{16}}.\sqrt{\dfrac{49}{9}}.\sqrt{\dfrac{1}{100}}=\dfrac{5}{4}.\dfrac{7}{3}\dfrac{1}{10}=\dfrac{7}{24}\)
b,\(\sqrt{1,44.1,21-1,44.0,4}=\sqrt{1,44.\left(1,21-0,4\right)}=\sqrt{1,44.0,81}=\sqrt{144}.\sqrt{0,81}=12.0,9=10,8\)
c,
\(\sqrt{\dfrac{165^2-124^2}{164}}=\sqrt{\dfrac{\left(165-124\right).\left(165+124\right)}{164}}=\sqrt{\dfrac{41.289}{164}}=\sqrt{\dfrac{289}{4}}=\dfrac{\sqrt{289}}{\sqrt{4}}=\dfrac{17}{4}\)
d, \(\sqrt{\dfrac{149^2-76^2}{457^2-384^2}}=\sqrt{\dfrac{\left(149-76\right)\left(149+76\right)}{\left(457-384\right)\left(457+384\right)}}=\sqrt{\dfrac{73.225}{73.841}}=\sqrt{\dfrac{225}{841}}=\dfrac{\sqrt{225}}{\sqrt{841}}=\dfrac{15}{29}\)
a)
.
b)
.
c)
.
d)
.
a, = \(\sqrt{\dfrac{25}{16}.\dfrac{49}{9}}.\dfrac{1}{100}\) = \(\sqrt{\dfrac{25}{16}}\). \(\sqrt{\dfrac{49}{9}}\) .\(\sqrt{\dfrac{1}{100}}\) = \(\dfrac{\sqrt{25}}{\sqrt{16}}\). \(\dfrac{\sqrt{49}}{\sqrt{9}}\).\(\dfrac{\sqrt{1}}{\sqrt{100}}\) = \(\dfrac{5}{4}\) . \(\dfrac{7}{3}\) .\(\dfrac{1}{10}\)= \(\dfrac{35}{120}\)=\(\dfrac{7}{24}\)
b, = \(\sqrt{1,44}.\left(1,21-0,4\right)\) = \(\sqrt{1,44}.0,8\) = \(\sqrt{\dfrac{144}{100}.\dfrac{81}{100}}\) = \(\sqrt{\dfrac{144}{100}}\).\(\sqrt{\dfrac{81}{100}}\)= \(\dfrac{\sqrt{144}}{\sqrt{100}}\).\(\dfrac{\sqrt{81}}{\sqrt{100}}\)
= \(\dfrac{12}{10}\). \(\dfrac{9}{10}\) =\(\dfrac{108}{100}\)=\(\dfrac{27}{25}\)
c, = \(\sqrt{\dfrac{\left(165-124\right).\left(165+124\right)}{164}}\)= \(\sqrt{\dfrac{41.289}{164}}\)= \(\sqrt{\dfrac{289}{4}}\)=\(\dfrac{\sqrt{289}}{\sqrt{4}}\)=\(\dfrac{17}{2}\)
d, = \(\sqrt{\dfrac{\left(149-76\right).\left(149+76\right)}{\left(457-384\right).\left(457+384\right)}}\)=\(\sqrt{\dfrac{73.225}{73.841}}\)=\(\sqrt{\dfrac{225}{841}}\)=\(\dfrac{\sqrt{225}}{\sqrt{841}}\)=\(\dfrac{15}{29}\)
a)
.
b)
.
c)
.
d)
.
a) = 7/24
b) = 27/25
c) = 17/2
d) = 15/29
a,\(\dfrac{7}{24}\)
b,1,08
c,\(\dfrac{17}{2}\)
d,\(\dfrac{15}{29}\)
a)
.
b)
.
c)
.
d)
.
a)\(\dfrac{7}{24}\)
b)\(1,08\)
c)\(\dfrac{17}{2}\)
d)\(\dfrac{15}{29}\)
a) \(\sqrt{1\dfrac{9}{16}\cdot5\dfrac{4}{9}\cdot0,01}\)
= \(\sqrt{\left(\dfrac{1\cdot16+9}{16}\right)\cdot\left(\dfrac{5\cdot9+4}{9}\right)\cdot\dfrac{1}{100}}\)
= \(\sqrt{\dfrac{25}{16}}\cdot\sqrt{\dfrac{49}{9}}\cdot\sqrt{\dfrac{1}{100}}\)
= \(\dfrac{\sqrt{25}}{\sqrt{16}}\cdot\dfrac{\sqrt{49}}{\sqrt{9}}\cdot\dfrac{\sqrt{1}}{\sqrt{100}}\)
= \(\dfrac{5}{4}\cdot\dfrac{7}{3}\cdot\dfrac{1}{10}\)
= \(\dfrac{7}{24}\)
b) \(\sqrt{1,44\cdot1,21-1,44\cdot0,4}\)
= \(\sqrt{1,44.\left(1,21-0,4\right)}\)
= \(\sqrt{1,44\cdot0,81}\)
= \(\sqrt{1,44}\cdot\sqrt{0,81}\)
= 1,2 . 0,9
= 1,08
c) \(\sqrt{\dfrac{165^2-124^2}{164}}\)
= \(\sqrt{\dfrac{\left(165-124\right)\left(165+124\right)}{164}}\)
= \(\sqrt{\dfrac{41\cdot289}{164}}\) = \(\sqrt{\dfrac{289}{4}}\) = \(\dfrac{\sqrt{289}}{\sqrt{4}}\) = \(\dfrac{17}{2}\)
d) \(\sqrt{\dfrac{149^2-76^2}{457^2-384^2}}\)
= \(\sqrt{\dfrac{\left(149-76\right)\left(149+76\right)}{\left(457-384\right)\left(457+384\right)}}\)
\(\sqrt{\dfrac{73\cdot225}{73\cdot841}}\) = \(\sqrt{\dfrac{225}{841}}\) = \(\dfrac{\sqrt{225}}{\sqrt{841}}\) = \(\dfrac{15}{29}\)
\(\sqrt{\dfrac{1.16+9}{16}.\dfrac{5.9+4}{9}.\dfrac{1}{100}}\) =\(\sqrt{\dfrac{25}{16}}.\sqrt{\dfrac{49}{9}}.\sqrt{\dfrac{1}{100}}\) =\(\dfrac{5}{4}.\dfrac{7}{3}.\dfrac{1}{10}\) =\(\dfrac{7}{24}\) b)\(\sqrt{1,44\left(1,21-0,4\right)}=\sqrt{1,44}.0,81\)
a, \(\dfrac{7}{24}\) ;b= 1,08 ;c=\(\dfrac{17}{2}\) ;d=\(\dfrac{15}{29}\)