Question

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

Answer 1

Answer:

The answer is Option 2 or B. 3√125x3

Step-by-step explanation:

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Answer 2

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

Step-by-step explanation: Given radical expression

$\sqrt[3]{5x} \times \sqrt[3]{25x^2}$.

According to the product property of roots.

$\sqrt[n]{a} \times \sqrt[n]{b} = \sqrt[n]{a \times b}$

On applying above rule, we get

$\sqrt[3]{5x} \times \sqrt[3]{25x^2} = \sqrt[3]{5x \times 25x^2}$

5 × 25 = 125 and

$x \times x^2 = x^3$

Therefore,

$\sqrt[3]{5x \times 25x^2}= \sqrt[3]{125x^3}$

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