Simplify the radical expression. Where appropriate, use absolute values.
√x20 y2 z10
just divide all the exponents by 2:
√(x^20 y^2 z^10) = x^10 y z^5
Why did the mathematician become a farmer? Because he wanted to simplify radicals and grow some roots! Now, let's simplify the radical expression √x^20 * y^2 * z^10.
We can break it down as follows:
√(x^10 * x^10) * (y * y) * z^10
The absolute value signs are not required here, as the expression inside the square root is already positive due to the even exponents. So, the simplified expression is:
|x^10| * |x^10| * |y| * |y| * z^10
This can be further reduced as x^10 * x^10 * y * y * z^10. Keep in mind that all variables have positive exponents, so there's no need for absolute values in this case!
To simplify the radical expression √(x^20 * y^2 * z^10), we can use the properties of radicals.
First, let's break down the factors inside the radical:
√(x^20 * y^2 * z^10) = √(x^20) * √(y^2) * √(z^10)
Now, we can simplify each factor individually:
√(x^20) = |x^10|
√(y^2) = |y|
√(z^10) = |z^5|
Putting it back together, we have:
√(x^20 * y^2 * z^10) = |x^10| * |y| * |z^5|
Therefore, the simplified radical expression is |x^10| * |y| * |z^5|.
To simplify the given radical expression √x^20 y^2 z^10 , we can break down each term under the square root and simplify it separately.
Let's start by breaking down each term under the square root:
x^20 = (x^10)^2
y^2 = (y^1)^2
z^10 = (z^5)^2
Now, taking the square root of each term, we have:
√x^20 y^2 z^10 = √((x^10)^2 * (y^1)^2 * (z^5)^2)
Next, we use the property of square roots to bring each term inside the radical that has an exponent of 2 outside the square root sign:
√x^20 y^2 z^10 = (x^10 * y * z^5)
Finally, if needed, we can use absolute value symbols where appropriate. Since the original expression does not involve any absolute values, the simplified radical expression is:
√x^20 y^2 z^10 = x^10 y z^5