# Operations with radicals

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###### Topic Notes

$\cdot$ even root: ${^{even}}\sqrt{positive}=defined$ i.e. $\sqrt{64}=8$

${^{even}}\sqrt{negative}=undefined$ i.e. $\sqrt{-64}=undefined$

$\cdot$ odd root: ${^{odd}}\sqrt{positive\;or\;negative}=defined$ i.e. ${^3}\sqrt{64}=4$

i.e. ${^3}\sqrt{-64}=-4$

${^{even}}\sqrt{negative}=undefined$ i.e. $\sqrt{-64}=undefined$

$\cdot$ odd root: ${^{odd}}\sqrt{positive\;or\;negative}=defined$ i.e. ${^3}\sqrt{64}=4$

i.e. ${^3}\sqrt{-64}=-4$

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