tex] ЗАРАНЕЕ БОЛЬШОЕ СПАСИБО!...

October 2021 1 7 Report

ВЫЧИСЛИТЕ
1)[tex] \sqrt{\frac{ \sqrt{65^{2}-56^{2} } }{ 57^{2}-24^{2} }}[/tex]
2)[tex] \sqrt{\frac{3,02^{2}-2,98^{2} }{ \sqrt{40^{2}-32 ^{2} }}[/tex]
ЗАРАНЕЕ БОЛЬШОЕ СПАСИБО!

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kirichekov

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$\sqrt{ \frac{ \sqrt{ 65^{2}- 56^{2} } }{ 57^{2} - 24^{2} } } = \sqrt{ \frac{ \sqrt{ (65-56)*(65+56)}}{(57-24)*(57+24)} } = \sqrt{ \frac{ \sqrt{9*121} }{33*81} } = \sqrt{ \frac{3*11}{3*11*9} } = \sqrt{ \frac{1}{9} } = \frac{1}{3}$
$\sqrt{ \frac{ 3,02^{2} - 2,98^{2}}{ \sqrt{ 40^{2} - 32^{2} } } } = \sqrt{ \frac{(3,02-2,98)*(3,02+2,98)}{ \sqrt{(40-32)*(40+32)} } } = \sqrt{ \frac{0,04*6}{ \sqrt{ 8*72} } }= \sqrt{ \frac{0,04*6}{ \sqrt{4*2*2*36} } } =$
$= \sqrt{ \frac{0,04*6}{4*6} } = \sqrt{0,01}=0,1$

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