Bài 32 trang 19 môn Toán 9 - tập 1, Bài 32. Tính...

Bài 32. Tính

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

b) $\sqrt{1,44.1,21-1,44.0,4}$;

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

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

Hướng dẫn giải:

a)

$\sqrt{1\frac{9}{16}.5\frac{4}{9}.0,01}=\sqrt{\frac{25}{16}.\frac{49}{9}}.\sqrt{0,01}$

$=\frac{5}{4}.\frac{7}{3}.0,1=\frac{3,5}{12}=\frac{7}{24}$

b)

$\sqrt{1,44.1,21-1,44.0,4}$

$=\sqrt{1,44(1,21-0,4)}$

$=\sqrt{1,44.0,81}$

$=\sqrt{1,44}.\sqrt{0,81}$

$=1,2.0,9=1,08$

c)

$\sqrt{\frac{165^{2}-124^{2}}{164}}$

$=\sqrt{\frac{(165-124)(165+124)}{164}}$

$=\sqrt{\frac{41.289}{41.4}}$

$=\sqrt{\frac{289}{4}}=\frac{17}{2}$

Câu d:

$\sqrt{\frac{149^{2}-76^{2}}{457^{2}-384^{2}}}$

$=\sqrt{\frac{(149-76)(149+76)}{(457-384)(457+384)}}$

$=\sqrt{\frac{73.225}{73.841}}$

$=\sqrt{\frac{225}{841}}=\frac{15}{29}$