Bài 32 (Trang 19 SGK Toán 9, Tập 1):

Tính:

$\mathrm{a}) \sqrt{1\frac{9}{16}.5\frac{4}{9}.0,01};$

$\mathrm{b}) \sqrt{1,44.1,21 - 1,44.0,4};$

$\mathrm{c}) \sqrt{\frac{{165}^2 - {124}^2}{164}};$

$\mathrm{d}) \sqrt{\frac{{149}^2 - {76}^2}{{457}^2 - {384}^2}}.$

Hướng dẫn giải:

$$\begin{gathered} \mathrm{a}) \sqrt{1\frac{9}{16}.5\frac{4}{9}.0,01} = \sqrt{\frac{1.16 + 19}{16}.\frac{5.9 + 4}{9}.\frac{1}{100}} \\ = \sqrt{\frac{16 + 19}{16} . \frac{45 + 4}{9} . \frac{1}{100}} \\ = \sqrt{\frac{25}{16}.\frac{49}{9}.\frac{1}{100}} = \sqrt{\frac{25}{16}} . \sqrt{\frac{49}{9}}. \sqrt{\frac{1}{100}} \\ = \frac{\sqrt{5^2}}{\sqrt{4^2}} . \frac{\sqrt{7^2}}{\sqrt{3^2}} . \frac{1}{\sqrt{{10}^2}} = \frac{5}{4}.\frac{7}{3}.\frac{1}{10} = \frac{7}{24}. \end{gathered}$$

$\mathrm{b}) \sqrt{1,44.1,21 - 1,44.0,4} = \sqrt{1,44.(1,21 - 0,4)} = \sqrt{1,44} . \sqrt{0,81} = \sqrt{1,2^2}.\sqrt{0,9^2} = 1,2.0,9 = 1,08.$

$\mathrm{c}) \sqrt{\frac{{165}^2 - {124}^2}{164}} = \sqrt{\frac{(165 - 124)(165 + 124)}{164}} = \sqrt{\frac{41.289}{41.4}} = \sqrt{\frac{289}{4}} = \frac{\sqrt{{17}^2}}{\sqrt{2^2}} = \frac{17}{2}.$

$\mathrm{d}) \sqrt{\frac{{149}^2 - {76}^2}{{457}^2 - {384}^2}} = \sqrt{\frac{(149 - 76)(149 + 76)}{(457 - 384)(457 + 384)}} = \sqrt{\frac{73.225}{73.874}} = \sqrt{\frac{225}{841}} = \frac{\sqrt{{15}^2}}{\sqrt{{29}^2}} = \frac{15}{29}.$