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Example Questions
Example Question #1151 : Act Math
Simplify:
To solve, simply find a perfect square factor and pull it out of the square root.
Recall the factors of 48 include (16, 3). Also recall that 16 is a perfect square since 4*4=16.
Thus,
Example Question #81 : Arithmetic
Solve:
The trick to these problems is to simplify the radical by using the following rule: and Here, we need to find a common factor for the radical. This turns out to be five because Remember, we want to include factors that are perfect squares, which are what nine and four are. Therefore, we can rewrite the equation as:
Example Question #16 : Exponents And Roots
Each of the following is equal to for all values of EXCEPT?
This question may look daunting, especially if you start out by trying pick values or and solving. This plan of attack will work, but you're likely going to be dealing with some messy numbers. Instead we want to recall some of our exponent and root rules.
Let's look at this answer choice:
This double square root is the same as a fourth root. Think about it, you have a square times a square- which is the same thing as . Thus, so this choice can be eliminated.
Next, let's look at this answer choice:
For this choice, we need to recall our exponent rules. Remember, whenever we have a value raised to a fractional power, the denominator of that fraction is equal to the root number. In this case, . Thus,
Now, let's look at this answer choice:
A key rule to remember here is that order doesn't not matter when dealing with roots and powers. Thus, taking the root of a number and then cubing it will result in the same value as cubing a number and then taking the root .
This leaves us with:
If we tried to break this down a bit, we could take the third root of , which would leave us with:
. This will not equal .
Example Question #172 : Equations / Inequalities
Hannah is selling candles for a school fundraiser all fall. She sets a goal of selling candles per month. The number of candles she has remaining for the month can be expressed at the end of each week by the equations , where is the number of candles and is the number of weeks she has sold candles this month. What is the meaning of the value in this equation?
The number of candles that she sells each week.
The number of candles she has remaining for the month.
The number of weeks that she has sold candles this month.
The number of candles that she has sold thus far that week.
The number of candles that she sells each week.
Since we know that stands for weeks, the answer has to have something to do with the weeks. This eliminates "the number of candles she has remaining for the month." Also, we can eliminate "the number of weeks that she has sold candles this month" because that would be our value for , not what we'd multiply by. The correct answer is, "the number of candles that she sells each week."