Question

simplify by combining similar terms:
$2 \sqrt[3]{4} + 7 \sqrt[3]{32} - \sqrt[3]{500}$




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Answer 1

♧︎︎︎ ǫᴜᴇsᴛɪᴏɴ ♧︎︎︎

➪ $2 \sqrt[3]{4} + 7 \sqrt[3]{32} - \sqrt[3]{500}$

♧︎︎︎ ᴀɴsᴡᴇʀ ♧︎︎︎

➪ʀᴇᴅᴜᴄɪɴɢ ɪɴᴛᴏ sɪᴍᴘʟᴇsᴛ ғᴏʀᴍ

$\sqrt[3]{32} = \sqrt[3]{2 {}^{3} \times {2}^{2} } = 2 \sqrt[3]{4}$

$\sqrt[3]{500} = \sqrt[3]{5 {}^{3} \times 2 {}^{2} } = 5 \sqrt[3]{4}$

ᴛʜᴇʀᴇ ғᴏʀᴇ:

$2 \sqrt[3]{4} + 7 \sqrt[3]{32} - \sqrt[3]{500} = 2 \sqrt[3]{4} + 7 \times 2 \sqrt[3]{4} - 5 \sqrt[3]{4}$

$= 2 \sqrt[3]{4} + 14 \sqrt[3]{4} - 5 \sqrt[3]{4}$

$= (2 + 14 - 5) \sqrt[3]{4}$

$11 \sqrt[3]{4}$

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