283. Найдите значение частного: a) \frac{\sqrt{2}}{\sqrt{18}} 6) \frac{\sqrt{23}}{\sqrt{2300}} в) \frac{\sqrt{52}}{\sqrt{117}} г) \frac{\sqrt{12500}}{\sqrt{500}}

Решение:

• a) \(\frac{\sqrt{2}}{\sqrt{18}} = \sqrt{\frac{2}{18}} = \sqrt{\frac{1}{9}} = \frac{1}{3}\)
• б) \(\frac{\sqrt{23}}{\sqrt{2300}} = \sqrt{\frac{23}{2300}} = \sqrt{\frac{1}{100}} = \frac{1}{10}\)
• в) \(\frac{\sqrt{52}}{\sqrt{117}} = \sqrt{\frac{52}{117}}\)
• Разделим числитель и знаменатель на 13: \(\frac{52}{117} = \frac{4 \times 13}{9 \times 13} = \frac{4}{9}\)
• \(\sqrt{\frac{4}{9}} = \frac{2}{3}\)
• г) \(\frac{\sqrt{12500}}{\sqrt{500}} = \sqrt{\frac{12500}{500}} = \sqrt{\frac{125}{5}} = \sqrt{25} = 5\)

Ответ:

• a) \(\frac{1}{3}\)
• б) \(\frac{1}{10}\)
• в) \(\frac{2}{3}\)
• г) 5