\(\sqrt{\dfrac{149^2-76^2}{457^2-384^2}}=\sqrt{\dfrac{\left(149-76\right)\left(149+76\right)}{\left(457-384\right)\left(457+384\right)}}\)

\(=\sqrt{\dfrac{73\cdot225}{73\cdot841}}=\sqrt{\dfrac{225}{841}}=\dfrac{15}{29}\)

\(\sqrt{\frac{149^2-76^2}{457^2-384^2}}=\sqrt{\frac{73.225}{73.841}}=\sqrt{\frac{225}{841}}=\frac{\sqrt{225}}{\sqrt{841}}=\frac{15}{29}\)

Ta có: \(A=\frac{3}{1\cdot5}+\frac{3}{5\cdot4}+\frac{3}{4\cdot11}+...+\frac{3}{73\cdot149}+\frac{3}{149\cdot76}\)

\(\Rightarrow A=\frac{1}{2}\cdot\left(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+...+\frac{3}{146\cdot149}+\frac{3}{149\cdot152}\right)\)

\(\Rightarrow A=\frac{1}{2}\cdot\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{146}-\frac{1}{149}+\frac{1}{149}-\frac{1}{152}\right)\)

\(\Rightarrow A=\frac{1}{2}\cdot\left(\frac{1}{2}-\frac{1}{152}\right)=\frac{1}{2}\cdot\left(\frac{76}{152}-\frac{1}{152}\right)=\frac{1}{2}\cdot\frac{75}{152}=\frac{75}{304}\)

1) \(\frac{\sqrt{165^2-124^2}}{164}=\frac{\sqrt{\left(165-124\right)\left(165+124\right)}}{164}=\frac{\sqrt{41}\cdot\sqrt{289}}{164}=\frac{\sqrt{41}\cdot17}{164}=\frac{17}{4\sqrt{41}}\)

2) \(\frac{\sqrt{149^2-76^2}}{\sqrt{457^2-384^2}}=\frac{\sqrt{\left(149+76\right)\left(149-76\right)}}{\sqrt{\left(457+384\right)\left(457-384\right)}}=\frac{\sqrt{225}\cdot\sqrt{73}}{\sqrt{841}\cdot\sqrt{73}}=\frac{25}{29}\)

a. \(678\times\left(276+49\right)-678\times\left(149+76\right)\)

\(=678\times\left[\left(276+49\right)-\left(149+76\right)\right]\)

\(=678\times\left(276+49-149-76\right)\)

\(=678\times\left(200-100\right)\)

\(=67800\)

b. \(23\times157+15\times46-28\times87\)

\(=3611+690-2436\)

\(=1865\)

c. \(12:\left\{390:\left[500-\left(125+35\times7\right)\right]\right\}\)

\(=12:\left\{390:\left[500-\left(125+245\right)\right]\right\}\)

\(=12:\left\{390:\left[500-370\right]\right\}\)

\(=12:\left\{390:130\right\}\)

\(=12:3\)

\(=4\)

678 . ( 276 + 49 ) - 678 . ( 149+76 ) = 678 . 325 - 678 . 225

                                                    = 678 . ( 325 - 225 )

                                                    = 678 . 100

                                                    =67800. 

a. =\(\sqrt{20.72.4,9}=\sqrt{2.72.49}=\sqrt{144.49}=12.7=84\)

b. \(\sqrt{\frac{999}{111}}=\sqrt{9}=3\)

c. = \(\sqrt{9472+27256}=\sqrt{36728}\approx191,645\)

d. = \(\sqrt{\frac{\left(149+76\right)\left(149-76\right)}{\left(457+348\right)\left(457-348\right)}}=\sqrt{\frac{225.73}{805.109}}=\sqrt{\frac{3285}{17549}}\approx136,817\)

a) \(\sqrt{\frac{\left(165-124\right)\left(165+124\right)}{164}}=\sqrt{\frac{41.289}{164}}=\sqrt{\frac{289}{4}}=\frac{17}{2}\)

b) tương tự ý a

c) \(\left(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\right)^2=7+4\sqrt{3}+7-4\sqrt{3}-2.\sqrt{7+4\sqrt{3}}.\sqrt{7-4\sqrt{3}}\)

\(=14-2\sqrt{\left(7+4\sqrt{3}\right)\left(7-4\sqrt{3}\right)}\)

\(=14-2\sqrt{49-48}\)

\(=14-2.1=12\)

\(\Rightarrow\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}=\sqrt{12}=2\sqrt{3}\)

a) HD: Đổi hỗn số và số thập phân thành phân số.

ĐS: .

b) =

= = =

= .

d) ĐS: .

a: \(=\sqrt{\dfrac{25}{16}\cdot\dfrac{49}{9}\cdot\dfrac{1}{100}}=\dfrac{5}{4}\cdot\dfrac{7}{3}\cdot\dfrac{1}{10}=\dfrac{35}{120}=\dfrac{7}{24}\)

b: \(=\sqrt{1.44\cdot0.81}=1.2\cdot0.9=1.08\)

c: \(=\sqrt{\dfrac{\left(165-124\right)\left(165+124\right)}{164}}=\sqrt{\dfrac{1}{4}\cdot289}=\dfrac{17}{2}\)

d: \(=\sqrt{\dfrac{\left(149-76\right)\left(149+76\right)}{\left(457-384\right)\left(457+384\right)}}=\sqrt{\dfrac{225}{841}}=\dfrac{15}{29}\)