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Question #ee927

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May 14, 2017

$- 6 \sqrt[7]{2} + 2 \sqrt[7]{256} = - 2 \sqrt[7]{2}$ $-6root(7)2+2root(7)(256)=color(red)(-2root(7)2$

Explanation:

I have assumed $\sqrt[7]{265}$ $root(7)(265)$ was meant to be $\sqrt[7]{256}$ $root(7)(256)$

$256 = 2^{8} = 2^{7} \cdot 2$ $256=2^8=2^7 * 2$

$\sqrt[7]{256} = \sqrt[7]{2^{7} \cdot 2} = \sqrt[7]{2^{7}} \cdot \sqrt[7]{2} = 2 \sqrt[7]{2}$ $color(blue)(root(7)(256))=root(7)(2^7 * 2) = root(7)(2^7) * root(7)(2)color(blue)(=2root(7)2)$

$- 6 \sqrt[7]{2} + 2 \sqrt[7]{256}$ $-6root(7)2+2color(blue)(root(7)(256)$
$XXX = - 6 \sqrt[7]{2} + 2 \cdot 2 \sqrt[7]{2}$ $color(white)("XXX")=-6root(7)(2)+2*color(blue)(2root(7)(2))$

$XXX = - 6 \sqrt[7]{2} + 4 \sqrt[7]{2}$ $color(white)("XXX")=-6root(7)(2)+4root(7)(2)$

$XXX = - 2 \sqrt[7]{2}$ $color(white)("XXX")=-2root(7)(2)$

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