Take a factor out of the square root:
√27c^6, where c <0
Well, since c is less than 0, we're going to need to include the negative sign outside the square root. So let's tackle the problem step by step:
First, let's find the largest perfect square that can be factored out of 27. That would be 9. So, we have:
√(9 * 3c^6)
Now, let's simplify this even further by factoring out the 9:
3c^3 * √3
And voila! We've factored out the square root of 27c^6, where c is less than 0. Now it's time for a math comedy routine – "Why don't scientists trust atoms? Because they make up everything!"
To take a factor out of the square root of √27c^6, where c < 0, we need to find the largest perfect square that can be divided into 27c^6.
First, let's break down 27 and c^6 into their prime factors:
27 = 3^3
c^6 = (c^2)^3
Now, let's re-write the square root of √27c^6 using the prime factors:
√27c^6 = √(3^3 * (c^2)^3)
Next, let's try to take out a factor from the square root. Since c < 0, we can take out a factor of c^2, which will become |c| because we need to remove the negative sign:
√(3^3 * (c^2)^3) = |c| * √(3^3 * (c^2)^1)
Now, we have |c| outside the square root, and inside the square root we have 3^3 * (c^2)^1.
Simplifying the expression, we get:
|c| * √(27 * c^2)
|c| * √(9 * 3 * c^2)
|c| * √(9 * 3) * √c^2
|c| * 3√3 * |c|
Therefore, the result is 3√3 * |c|.
To take a factor out of the square root √27c^6 where c < 0, we need to find the largest perfect square that can be factored out from 27c^6. In this case, the largest perfect square that can be factored out is 9, which is a perfect square of 3.
Step 1: Identify the largest perfect square factor
In this case, the largest perfect square factor is 9.
Step 2: Rewrite the expression using the identified factor
√27c^6 can be rewritten as √(9 * 3 * c^6).
Step 3: Simplify the square root
Now, we can take the square root of the perfect square factor and place it outside the square root symbol:
3√(3 * c^6).
Therefore, the expression √27c^6 when c < 0 can be simplified as 3√(3 * c^6).
Did you mean √(27c^6) ?
√(27c^6)
= √9√3 √c^6
= 3√3 |c^3| , the √ symbol means, "take the principal root", which is positive