# How do you simplify #sqrt(3x) *sqrt(8x^3)#?

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To simplify the expression sqrt(3x) * sqrt(8x^3), we can use the property of square roots which states that the square root of a product is equal to the product of the square roots.

Therefore, we can simplify the expression as follows:

sqrt(3x) * sqrt(8x^3) = sqrt(3x * 8x^3)

Next, we can simplify the product inside the square root:

sqrt(3x * 8x^3) = sqrt(24x^4)

Since 24 can be factored into 4 * 6 and x^4 can be written as (x^2)^2, we can simplify further:

sqrt(24x^4) = sqrt(4 * 6 * (x^2)^2)

Using the property of square roots again, we can separate the square root of the product:

sqrt(4 * 6 * (x^2)^2) = sqrt(4) * sqrt(6) * sqrt((x^2)^2)

Simplifying further:

sqrt(4) * sqrt(6) * sqrt((x^2)^2) = 2 * sqrt(6) * x^2

Therefore, the simplified expression is 2 * sqrt(6) * x^2.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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