Question

Use the product property of roots to choose the expression equivalent to 3√5x*3√25x^2?

√30x
3√125x3
3√30x^2
6√125x^3

Answer 1

The answer is Option 2 or B. 3√125x3

Explanation:

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Answer 2

Answer:
`\sqrt[3]{125x^3}`.

Step-by-step explanation: Given radical expression

`\sqrt[3]{5x} * \sqrt[3]{25x^2}`.

According to the product property of roots.

`\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{a * b}`

On applying above rule, we get

`\sqrt[3]{5x} * \sqrt[3]{25x^2} = \sqrt[3]{5x * 25x^2}`

5 × 25 = 125 and

`x * x^2 = x^3`

Therefore,

`\sqrt[3]{5x * 25x^2}= \sqrt[3]{125x^3}`

So, the correct option would be second option
`\sqrt[3]{125x^3}`.