Question

Пж
Найдите значение корня:
√81; √0,04; √81/4; √2¼; √1 24/25; √1 7/9;
√2500; √0,25
​

Answer 1

$\sqrt{81}=9\\ \sqrt{0,04}=0,2\\ \sqrt{\frac{81}{4} } =\frac{9}{2}=4 \frac{1}{2}\\ \sqrt{2\frac{1}{4} } =\sqrt{\frac{9}{4} } =\frac{3}{2}=1 \frac{1}{2} \\ \sqrt{1 \frac{24}{25} } =\sqrt{\frac{49}{25} }=\frac{7}{5}=1 \frac{2}{5} \\\sqrt{1\frac{7}{9} } =\sqrt{\frac{16}{9} } =\frac{4}{3}=1 \frac{1}{3}\\ \sqrt{2500}=50\\ \sqrt{0,25}=0,5$

Answer 2

$\sqrt{81} = \sqrt{9 \times 9} = 9$

$\sqrt{0.04} = \sqrt{0.2 \times 0.2} = 0.2$

$\sqrt{ \frac{81}{4} } = \sqrt{ \frac{9 \times 9}{2 \times 2} } = \frac{ \sqrt{9 \times 9} }{ \sqrt{2 \times 2} } = \frac{9}{2} = 4.5$

$\sqrt{2 \frac{1}{4} } = \sqrt{ \frac{2 \times 4 + 1}{4} } = \sqrt{ \frac{9}{4} } = \frac{ \sqrt{9} }{ \sqrt{4} } = \frac{ \sqrt{3 \times 3} }{ \sqrt{2 \times 2} } = \frac{ 3 }{2} = 1.5$

$\sqrt{1 \frac{24}{25} } = \sqrt{ \frac{25 \times 1 + 24}{25} } = \sqrt{ \frac{49}{25} } = \frac{ \sqrt{49} }{ \sqrt{25} } = \frac{ \sqrt{7 \times 7} }{ \sqrt{5 \times 5} } = \frac{7}{5} = 1.4$

$\sqrt{1 \frac{7}{9} } = \sqrt{ \frac{9 \times 1 + 7}{9} } = \sqrt{ \frac{16}{9} } = \frac{ \sqrt{16} }{ \sqrt{9} } = \frac{ \sqrt{4 \times 4} }{ \sqrt{3 \times 3} } = \frac{4}{3}$

$\sqrt{2500} = \sqrt{50 \times 50} = 50$

$\sqrt{0.25} = \sqrt{0.5 \times 0.5} = 0.5$