Question

Найдите значение корня √145.5²-96.5²/193.5²-31.5²

Answer 1

$\sqrt{ \frac{ {(145.5)}^{2} - {(96.5)}^{2} }{ {(193.5)}^{2} - {(31.5)}^{2} } } = \sqrt{ \frac{(145.5 - 96.5)(145.5 + 96.5)}{(193.5 - 31.5)(193.5 + 31.5)} } = \sqrt{ \frac{49 \times 242}{162 \times 225} } = \sqrt{ \frac{49 \times 121}{81 \times 225} } = \frac{ \sqrt{49 \times 121} }{ \sqrt{81 \times 225} } = \frac{ \sqrt{49} \times \sqrt{121} }{ \sqrt{81} \times \sqrt{225} } = \frac{7 \times 11}{9 \times 15} = \frac{77}{135}$