PSAT Math : How to factor a common factor out of squares
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Example Questions
Example Question #2 : Squaring / Square Roots / Radicals
x2 = 36
Quantity A: x
Quantity B: 6
Quantity B is greater
The two quantities are equal
Quantity A is greater
The relationship cannot be determined from the information given
The relationship cannot be determined from the information given
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.
Example Question #1 : Squaring / Square Roots / Radicals
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?
4√14
48√77
8√14
14√2
12√5
8√14
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.
Example Question #181 : New Sat
Simplify the radical expression.
Look for perfect cubes within each term. This will allow us to factor out of the radical.
Simplify.
Example Question #1 : How To Factor A Common Factor Out Of Squares
Simplify the expression.
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.
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