Question

Thực hiện phép tính

a,\(\left(2-\dfrac{3}{4}\right)^2:\dfrac{11}{16}\)

b,\(2^3.\dfrac{7}{20}+\dfrac{7}{10}\)

c,\(\sqrt{3^2+4^2-\sqrt{1^3+2^3+3^3}}\)

d,\(21^3:\left(-7\right)^3\)

Answer 1

a,\(\left(2-\dfrac{3}{4}\right)^2:\dfrac{11}{6}=\left(\dfrac{5}{4}\right)^2:\dfrac{11}{6}=\dfrac{75}{88}\)

b,\(2^3.\dfrac{7}{20}+\dfrac{7}{10}=8.\dfrac{7}{20}+\dfrac{7}{10}=\dfrac{14}{5}+\dfrac{7}{10}=\dfrac{7}{2}\)

c, \(\sqrt{3^2+4^2-\sqrt{1^3+2^3+3^3}=}\sqrt{9+16-6}\)

\(=\sqrt{19}\)

d, \(21^3:\left(-7\right)^3=\left[21:\left(-7\right)\right]^3=\left(-3\right)^3=-27\)

Answer 2

a) \(\left(2-\dfrac{3}{4}\right)^2\): \(\dfrac{11}{16}\) = \(\left(\dfrac{8}{4}-\dfrac{3}{4}\right)^2:\dfrac{11}{16}\)

= \(\left(\dfrac{5}{4}\right)^2:\dfrac{11}{16}\)

= \(\dfrac{25}{16}:\dfrac{11}{16}=\dfrac{25}{16}.\dfrac{16}{11}=\dfrac{25}{11}\)

b) \(2^3.\dfrac{7}{20}+\dfrac{7}{10}\) = \(8.\dfrac{7}{20}+\dfrac{7}{10}=\dfrac{14}{5}+\dfrac{7}{10}\)

= \(\dfrac{28}{10}+\dfrac{7}{10}=\dfrac{7}{2}=3,5\)

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

= \(\sqrt{9+16-\sqrt{1+8+27}}\)

= \(\sqrt{9+16-\sqrt{36}}=\sqrt{9+16-6}\)

= \(\sqrt{19}\)

d) \(21^3:\left(-7\right)^3=\left[21:\left(-7\right)\right]^3=\left(-3\right)^3=-27\)