Complex Operations - GED Math
Card 0 of 1125
Simplify:
Simplify:
Start by simplifying each radical.
Now each radical is in terms of 
.
Add them together.
Start by simplifying each radical.
Now each radical is in terms of
Add them together.
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Simplify:
Simplify:
Start by simplifying each radical:
Notice that each radical simplifies down into a multiple of 
. Now add up these values to simplify.
Start by simplifying each radical:
Notice that each radical simplifies down into a multiple of
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Simplify 
.
Simplify
When simplifying a square root, you must break up what's inside the square root into its simplest factors. For example 
would break up to 
. Once you do that, you look for pairs of numbers. For each pair, you pull out the common number to the outside of the square root and leave whatever is left over inside the square root. So, for 
, you would break that up to 
and then 
. As you can see, there is a pair of 
, so you pull out a 
and leave whatever is left inside. Since the 
is left over you would leave that inside the square root. So, you have a 
outside the square root and a 
inside the square root, which gives you 
.
When simplifying a square root, you must break up what's inside the square root into its simplest factors. For example
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Solve for 
: 
Solve for
In order to solve for 
, our first priority is to get all the variables to one side so that 
is by itself. And luckily for us the problem already has all of the variables to to the other side.
Our next step then is to make sure 
is naked, meaning that there is nothing attached to the 
. We can see that our 
is not naked and is within a square root.
In order to get rid of the square root, we must square both sides of the equation The square root and square will cancel each other out, freeing the 
.
Since the right side of the equation needs to be squared, we have to foil 
in order to properly distribute the square.
can be also written as 
Foil the equation.
and 
can be classified as the same as it would be like writing 
and 
, so we can combine the two.
Let's bring back our 
since there is nothing more we can do to this equation.
Our answer is 
In order to solve for
Our next step then is to make sure
In order to get rid of the square root, we must square both sides of the equation The square root and square will cancel each other out, freeing the
Since the right side of the equation needs to be squared, we have to foil
Foil the equation.
Let's bring back our
Our answer is
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Solve for 
: 
Solve for
In order to solve for 
, we need to have all the variables on one side that isn't 
. Lucky for us our only other variable, 
, is on the other side of the equation.
Our next step then is to make sure 
is naked, meaning that there is nothing attached to our variable in order to solve it. We can see that our 
is encased in a square root, so we will need to get it out of there first.
In order to get rid of the square root, we will need to square the entire equation. The square and square root will cancel each other, releasing the 
.
We can now stop, as there is nothing else we can do to this equation because 
is the lowest we can go.
Our answer is 
In order to solve for
Our next step then is to make sure
In order to get rid of the square root, we will need to square the entire equation. The square and square root will cancel each other, releasing the
We can now stop, as there is nothing else we can do to this equation because
Our answer is
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Solve for 
:
Solve for
In order to solve for 
, we need to move all the variables beside it to the other side of the equation. Luckily for us 
is all by itself.
Our next step then is to make sure 
is naked, meaning nothing it attached to it. We can see though that our 
is being squared, so we need to get rid of that in order to proceed.
In order to get rid of the square, we must square root the whole equation. The square root and square will cancel each other out.
Since we don't have any variables that are the same, this is as far as we can go.
Our answer is 
In order to solve for
Our next step then is to make sure
In order to get rid of the square, we must square root the whole equation. The square root and square will cancel each other out.
Since we don't have any variables that are the same, this is as far as we can go.
Our answer is
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Solve for 
: 
Solve for
In order to solve for 
, we need to move all of the variables on its side of the equation over to the other side of the equation.
We can see that our 
is hiding in a square root, so in order to get the 
out we will need to square the whole equation.
Because we're multiply a power of 
with the power of 
, the two can multiply together to create a power of 
We can't do anything else to this equation as there are no like variables.
Our answer is 
In order to solve for
We can see that our
Because we're multiply a power of
We can't do anything else to this equation as there are no like variables.
Our answer is
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Solve for 
: 
Solve for
In order to solve for 
, we need to move all of the variables on its side over to the other side. We can see that our 
is being squared. In order to get rid of that square, we will need to square root the whole equation, as the square and square root will cancel out.
Because this is a square root of 
, our 
is like saying we have 
's. A square root can divide to the power of 
by 
, which leaves us with 
. The square root will also disappear for the 
because it has divided it.
We cannot go any further into this equation as there are no like variables to put together.
Our answer is 
In order to solve for
Because this is a square root of
We cannot go any further into this equation as there are no like variables to put together.
Our answer is
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Simplify:
Simplify:
Start by simplifying each radical.
The radicals all simplify down into multiples of 
. You can add them together.
Start by simplifying each radical.
The radicals all simplify down into multiples of
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Express as a decimal: 
Express as a decimal:
Divide 11 by 12:
The "6" repeats forever, so
.
Divide 11 by 12:
The "6" repeats forever, so
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Express as a fraction:
Express as a fraction:
Let 
Then
and
We can subtract:
Let
Then
and
We can subtract:
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Express as a decimal: 
Express as a decimal:
Divide 15 by 16:
Divide 15 by 16:
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Express as a fraction: 
Express as a fraction:
Let 
Then 
Subtract:
Let
Then
Subtract:
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Express as a decimal: 
Express as a decimal:
Divide 16 by 15:
The "6" repeats forever, so
.
Divide 16 by 15:
The "6" repeats forever, so
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Express as a decimal: 
Express as a decimal:
Divide 12 by 11:
The "09" repeasts forever, so
.
Divide 12 by 11:
The "09" repeasts forever, so
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Which number has 5.25 as its reciprocal?
Do not use a calculator.
Which number has 5.25 as its reciprocal?
Do not use a calculator.
The number that has 5.25 as its reciprocal is, in return, the reciprocal of 5.25.
Convert 5.25 to a fraction:
Switch the numerator and the denominator to obtain the reciprocal - this number is 
.
The number that has 5.25 as its reciprocal is, in return, the reciprocal of 5.25.
Convert 5.25 to a fraction:
Switch the numerator and the denominator to obtain the reciprocal - this number is
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Which of the following numbers has 
as its reciprocal?
Do not use a calculator.
Which of the following numbers has
Do not use a calculator.
The number that has 
as its reciprocal is, in return, the reciprocal of 
. This number is the result of switching the numerator and denominator - 
. Since we are looking for the decimal equivalent, we divide 29 by 8:
, the correct choice.
The number that has
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What is the decimal represented by the fraction 
?
What is the decimal represented by the fraction
Set up a proportion such that this fraction is some number over 100.
Cross multiply.
Divide by 50 on both sides.
The answer is: 
Set up a proportion such that this fraction is some number over 100.
Cross multiply.
Divide by 50 on both sides.
The answer is:
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Which of the following represents the equivalent of 
?
Which of the following represents the equivalent of
You can convert 
to the fraction:
After you do this, you then need to simplify. You can divide out of numerator and denominator the value 
, giving you:
You can convert
After you do this, you then need to simplify. You can divide out of numerator and denominator the value
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Which of the following is equivalent to 
?
Which of the following is equivalent to
You can begin by converting 
into the fraction:
Now, you can begin canceling from the numerator and the denominator. You are looking for factors of 
. The denominator is only made up of 
and 
factors (because it is a power of 
). The denominator is really merely: 
. This means that it has a total of four 
s. That is the same as 
. Does the numerator have this many twos? You can try to figure that out by dividing it by 
. It does! This gets you the value 
. Therefore, you will have:
, or 
You can begin by converting
Now, you can begin canceling from the numerator and the denominator. You are looking for factors of 
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