Take a factor out of the square root:

square root of 10y^2 , where y<0

since √y^2 = |y|, if y<0, then

√10y^2 = -y√10

To take a factor out of the square root of 10y^2, where y < 0, 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 of the factors.

First, let's identify the factors of 10y^2. The factors are 10 and y^2.

square root of 10y^2 = square root of (10 * y^2)

Using the property mentioned earlier, we can write this as:

square root of 10y^2 = square root of 10 * square root of y^2

The square root of 10 is a constant and cannot be simplified further, so we keep it outside the square root:

√10 * square root of y^2

Now, let's simplify the square root of y^2. The square root of y^2 is equal to the absolute value of y, since y is negative.

√10 * |y|

Therefore, the simplified form of the square root of 10y^2, where y < 0, is √10 * |y|.

To take a factor out of the square root, you need to identify the perfect square factors inside the square root.

In the given expression, the square root of 10y^2 can be written as the product of two separate square roots: the square root of 10 and the square root of y^2.

Let's break down the steps to find the answer:

Step 1: Identify any perfect square factors inside the given expression. In this case, y^2 is a perfect square because y is raised to the power of 2.

Step 2: Take the square root of the perfect square factor. The square root of y^2 is equal to y because when we square y, we get y^2.

Step 3: Express the original expression as the product of the square root of the perfect square factor and the square root of the remaining factors. Therefore, the square root of 10y^2 can be written as the product of the square root of 10 and y: √10 * √y.

So, the factor that can be taken out of the square root of 10y^2, where y < 0, is y. The result is √10 * y.