Question

`5 * \sqrt[3]{24} + 7 * \sqrt[3]{375} - 2 * \sqrt[3]{81}`

necesito los cálculos auxiliares de este problema ​

Answer 1

The value of this expression when simplified is
`39\sqrt[3]{3}`

How to determine the expression

By simplifying,

`5*\sqrt[3]{24}+7 *\sqrt[3]{375} -2*\sqrt[3]{81}`

First, identifying the perfect cubes within each radical and then simplify.

`\sqrt[3]{24}` =
`\sqrt[3]{2^(3) *3}`

`\sqrt[3]{375}` =
`\sqrt[3]{5^(3) *3}`

`\sqrt[3]{81}` =
`\sqrt[3]{3^(3)*3}`

Comparing them,

5 *
`\sqrt[3]{2^(3) *3}` + 7 *
`\sqrt[3]{5^(3) *3}` - 2 *
`\sqrt[3]{3^(3)*3}`

5 *
`2\sqrt[3]{3}` + 7 *
`5\sqrt[3]{3}`- 2 *
`3\sqrt[3]{3}`

`10\sqrt[3]{3}` +
`35\sqrt[3]{3}` -
`6\sqrt[3]{3}`

=
`39\sqrt[3]{3}`

Therefore, the value of this expression when simplified is
`39\sqrt[3]{3}`