All PSAT Math Resources
Example Questions
Example Question #1 : How To Simplify Square Roots
Simplify. Assume all variables are positive real numbers.
The index coefficent in is represented by . When no index is present, assume it is equal to 2. under the radical is known as the radican, the number you are taking a root of.
First look for a perfect square,
Then to your Variables
Take your exponents on both variables and determine the number of times our index will evenly go into both.
So you would take out a and would be left with a
*Dividing the radican exponent by the index - gives you the number of variables that should be pulled out.
The final answer would be .
Example Question #1 : How To Simplify Square Roots
Simplify. Assume all integers are positive real numbers.
Index of means the cube root of Radican
Find a perfect cube in
Simplify the perfect cube, giving you .
Take your exponents on both variables and determine the number of times our index will evenly go into both.
The final answer would be
Example Question #4 : Factoring And Simplifying Square Roots
Simplify square roots. Assume all integers are positive real numbers.
Simplify as much as possible. List all possible answers.
1a.
1b.
1c.
and and
and and
and and
and
and and
When simplifying radicans (integers under the radical symbol), we first want to look for a perfect square. For example, is not a perfect square. You look to find factors of to see if there is a perfect square factor in , which there is.
1a.
Do the same thing for .
1b.
1c.Follow the same procedure except now you are looking for perfect cubes.
Example Question #1 : How To Simplify Square Roots
Simplify
9 ÷ √3
3√3
3
2
not possible
none of these
3√3
in order to simplify a square root on the bottom, multiply top and bottom by the root
Example Question #2 : Simplifying Square Roots
Simplify:
√112
12
10√12
20
4√7
4√10
4√7
√112 = {√2 * √56} = {√2 * √2 * √28} = {2√28} = {2√4 * √7} = 4√7
Example Question #1 : Simplifying Square Roots
Simplify:
√192
√192 = √2 X √96
√96 = √2 X √48
√48 = √4 X√12
√12 = √4 X √3
√192 = √(2X2X4X4) X √3
= √4X√4X√4 X √3
= 8√3
Example Question #1 : Simplifying Square Roots
What is the simplest way to express ?
First we will list the factors of 3888:
Example Question #2 : How To Simplify Square Roots
Simplify:
4√27 + 16√75 +3√12 =
4*(√3)*(√9) + 16*(√3)*(√25) +3*(√3)*(√4) =
4*(√3)*(3) + 16*(√3)*(5) + 3*(√3)*(2) =
12√3 + 80√3 +6√3= 98√3
Example Question #1 : How To Simplify Square Roots
Simplify:
To simplify a square root, you can break the number down into its prime factors using a factor tree. The prime factors of 72 are . Let's take each piece separately.
The square root of can be simplified to be which is the same as .
The square root of is .
When you multiply together your answers,
Example Question #21 : How To Find Absolute Value
If , what is the value of ?
Substitute – 4 in for x. Remember that when a negative number is raised to the third power, it is negative. - = – 64. – 64 – 36 = – 100. Since you are asked to take the absolute value of – 100 the final value of f(-4) = 100. The absolute value of any number is positive.
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