Question

найдите значение выражений

Answer 1

№1.

а)

$0.5 \sqrt{0.04} + \frac{1}{6} \sqrt{144} = 0.5 \times 0.2 + \frac{12}{6} = 0.1 + 2 = 2.1$

б)

$2 \sqrt{1 \frac{9}{16} } - 1 = 2 \sqrt{ \frac{25}{16} } - 1 = \frac{10}{4} - 1 = 2.5 - 1 = 1.5$

в)

${(2 \sqrt{0.5)} }^{2} = 4 \times 0.5 = 2$

№2.

а)

$\sqrt{0.25 \times 64} = 0.5 \times 8 = 4$

б)

$\sqrt{56} \times \sqrt{14} = \sqrt{56 \times 14} = \sqrt{784} = 28$

в)

$\frac{ \sqrt{8} }{ \sqrt{2} } = \frac{ \sqrt{4 \times 2} }{ \sqrt{2} } = \frac{2 \sqrt{2} }{ \sqrt{2} } = 2$

г)

$\sqrt{ {3}^{4} } \times \sqrt{ {2}^{6} } = \sqrt{81} \times \sqrt{64} = 9 \times 8 = 72$

№3.

а)

${x}^{2} = 0.49 \\ x_{1.2}= \sqrt{0.49} \\ x_{1} = 0.7 \\ x_{2} = - 0.7$

б)

${x}^{2} = 10 \\ x_{1.2}= \sqrt{10} \\ x_{1} = - \sqrt{10} \\ x_{2} = \sqrt{10}$

№4.

а)

$\sqrt{45} = 3 \sqrt{5}$

б)

$\sqrt{52} = 2 \sqrt{13}$

в)

$\sqrt{75} = 5 \sqrt{3}$

г)

$- \frac{1}{3} \sqrt{27} = - \frac{1}{3} \times 3 \sqrt{3} = - 1 \sqrt{3}$

д)

$\frac{2}{7} \sqrt{98} = \frac{2}{7} \times 7 \sqrt{2} = 2 \sqrt{2}$

№5.

а)

$3 \sqrt{5} > \sqrt{42} \\ \sqrt{45} > \sqrt{42}$

б)

$6 \sqrt{2} > 2 \sqrt{6} \\ \sqrt{72} > \sqrt{24}$