I need help! Simplifying radical expressions 1) \sqrt[3]{135} 2) - 5 {}^(3) √(40) 3) {2}^(3) √(5) * {4}^(3) √(8)

Question

I need help!

Simplifying radical expressions

1)

`\sqrt[3]{135}`
2)

`- 5 {}^(3) √(40)`
3)

`{2}^(3) √(5) * {4}^(3) √(8)`

Answer 1

Here is the solution...

1)
`\sqrt[3]{135} \\`

Solution

We can rewrite
`\sqrt[3]{135} = \sqrt[3]{27} *\sqrt[3]{5}`

Here,
`\sqrt[3]{27} = 3`

Now substitute the value, we get

`\sqrt[3]{135} = 3 \sqrt[3]{5}`

The answer is
`3\sqrt[3]{5}`

2)
`-5\sqrt[3]{40} </p><p><strong>Solution</strong></p><p>[tex]-5\sqrt[3]{40} = -5\sqrt[3]{8} *\sqrt[3]{5}`

Here
`\sqrt[3]{8} = \sqrt[3]{2^(3) } = 2\\`

Therefore, we get
`-5*2\sqrt[3]{5} = -10 \sqrt[3]{5}`

The answer is-10 \sqrt[3]{5}[/tex]

2)
`2\sqrt[3]{5} * 4\sqrt[3]{8}`

Solution

`\sqrt[3]{8} = 2`

Now plug in the above in the given expression, we get

`2\sqrt[3]{5} * 4*2 = 16\sqrt[3]{5}` {2*4*2 = 16]

The answer is
`16\sqrt[3]{5}`