How to factor a common factor out of squares
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PSAT Math › How to factor a common factor out of squares
Simplify the radical expression.
Explanation
Look for perfect cubes within each term. This will allow us to factor out of the radical.
Simplify.
According to Heron's Formula, the area of a triangle with side lengths of a, b, and c is given by the following:
where s is one-half of the triangle's perimeter.
What is the area of a triangle with side lengths of 6, 10, and 12 units?
12√5
4√14
8√14
14√2
48√77
Explanation
We can use Heron's formula to find the area of the triangle. We can let a = 6, b = 10, and c = 12.
In order to find s, we need to find one half of the perimeter. The perimeter is the sum of the lengths of the sides of the triangle.
Perimeter = a + b + c = 6 + 10 + 12 = 28
In order to find s, we must multiply the perimeter by one-half, which would give us (1/2)(28), or 14.
Now that we have a, b, c, and s, we can calculate the area using Heron's formula.
x2 = 36
Quantity A: x
Quantity B: 6
Quantity A is greater
Quantity B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Explanation
x2 = 36 -> it is important to remember that this leads to two answers.
x = 6 or x = -6.
If x = 6: A = B.
If x = -6: A < B.
Thus the relationship cannot be determined from the information given.
Simplify the expression.
Explanation
Use the distributive property for radicals.
Multiply all terms by 
Combine terms under radicals.
Look for perfect square factors under each radical. 
Since both radicals are the same, we can add them.
