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1.
[latex] \sqrt{0.5*50}= \sqrt{25}=5 \\ -2 \sqrt{5}* \sqrt{20}=-2 \sqrt{5}* \sqrt{4*5}=-2 \sqrt{5}*2 \sqrt{5}=-4*5=-20 \\ \sqrt{3}*4 \sqrt{27}= \sqrt{3}*4 \sqrt{9*3}= \sqrt{3}*4*3 \sqrt{3}=12*3=36 [/latex]
2.
[latex] \frac{- \sqrt{1000} }{ \sqrt{250} }= -\frac{\sqrt{4*250} }{ \sqrt{250} }=- \frac{2 \sqrt{250} }{250}=-2 \\ \sqrt{ \frac{144}{64} }= \sqrt{ \frac{9}{4}}= \frac{3}{2}=1.5 \\ \frac{ \sqrt{4^3*10^3} }{ \sqrt{1000} }= \frac{ \sqrt{64} * \sqrt{10^3} }{ \sqrt{10^3} } =8 [/latex]
3.
[latex] \sqrt{61^2-60^2}= \sqrt{(61-60)(61+60)}= \sqrt{1*121}=11 \\ \sqrt{5^2+12^2}= \sqrt{25+144}= \sqrt{169}=13 \\ \sqrt{(1 \frac{1}{25})^2-( \frac{2}{5})^2}= \sqrt{( \frac{26}{25})^2 -( \frac{2}{5})^2 }= \sqrt{( \frac{26}{25}- \frac{2}{5})( \frac{26}{25}+ \frac{2}{5})}= \sqrt{ \frac{16}{25}* \frac{36}{25} }= \\ \\ \sqrt{ \frac{24}{25} }= \frac{2}{5} \sqrt{3} [/latex]
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