How to find the common factors of squares - GRE Quantitative Reasoning
Card 1 of 112
Simplify:
Simplify:
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When simplifying the square root of a number that may not have a whole number root, it's helpful to approach the problem by finding common factors of the number inside the radicand. In this case, the number is 24,300.
What are the factors of 24,300?
24,300 can be factored into:
When there are factors that appear twice, they may be pulled out of the radicand. For instance, 100 is a multiple of 24,300. When 100 is further factored, it is 
(or 10x10). However, 100 wouldn't be pulled out of the radicand, but the square root of 100 because the square root of 24,300 is being taken. The 100 is part of the24,300. This means that the problem would be rewritten as: 
But 243 can also be factored: 
Following the same principle as for the 100, the problem would become
because there is only one factor of 3 left in the radicand. If there were another, the radicand would be lost and it would be 9*10*3.
9 and 10 may be multiplied together, yielding the final simplified answer of
When simplifying the square root of a number that may not have a whole number root, it's helpful to approach the problem by finding common factors of the number inside the radicand. In this case, the number is 24,300.
What are the factors of 24,300?
24,300 can be factored into:
When there are factors that appear twice, they may be pulled out of the radicand. For instance, 100 is a multiple of 24,300. When 100 is further factored, it is
But 243 can also be factored:
Following the same principle as for the 100, the problem would become
9 and 10 may be multiplied together, yielding the final simplified answer of
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Tap to reveal answer
To solve the equation 
, we can first factor the numbers under the square roots.
When a factor appears twice, we can take it out of the square root.
Now the numbers can be added directly because the expressions under the square roots match.
To solve the equation
When a factor appears twice, we can take it out of the square root.
Now the numbers can be added directly because the expressions under the square roots match.
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Simplify.
Simplify.
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To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 624 and is also a perfect square.
Therefore we can rewrite the square root of 624 as:
To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 624 and is also a perfect square.
Therefore we can rewrite the square root of 624 as:
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Reduce 
to its simplest form.
Reduce
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To simplify, we must try to find factors which are perfect squares. In this case 20 is a factor of 400 and is also a perfect square.
Thus we can rewrite the problem as:
Note: 
To simplify, we must try to find factors which are perfect squares. In this case 20 is a factor of 400 and is also a perfect square.
Thus we can rewrite the problem as:
Note:
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Simplify.
Simplify.
Tap to reveal answer
Use the following steps to reduce this square root.
To simplify, we must try to find factors which are perfect squares. In this case 144 is a factor of 720 and is also a perfect square.
Thus we can rewrite the problem as follows.
Use the following steps to reduce this square root.
To simplify, we must try to find factors which are perfect squares. In this case 144 is a factor of 720 and is also a perfect square.
Thus we can rewrite the problem as follows.
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Find the square root of 
.
Find the square root of
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Use the following steps to find the square root of 
To simplify, we must try to find factors which are perfect squares. In this case 900 is a factor of 1800 and is also a perfect square.
Thus we can rewrite the problem as follows.
Use the following steps to find the square root of
To simplify, we must try to find factors which are perfect squares. In this case 900 is a factor of 1800 and is also a perfect square.
Thus we can rewrite the problem as follows.
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Simplify.
Simplify.
Tap to reveal answer
To simplify, we must try to find factors which are perfect squares. In this case 9 is a factor of 54 and is also a perfect square.
To reduce this expression, use the following steps:
To simplify, we must try to find factors which are perfect squares. In this case 9 is a factor of 54 and is also a perfect square.
To reduce this expression, use the following steps:
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Reduce.
Reduce.
Tap to reveal answer
To simplify, we must try to find factors which are perfect squares. In this case 36 is a factor of 72 and is also a perfect square.
To reduce this expression, use the following arithmetic steps:
To simplify, we must try to find factors which are perfect squares. In this case 36 is a factor of 72 and is also a perfect square.
To reduce this expression, use the following arithmetic steps:
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Which quantity is greater: 
or 
?
Which quantity is greater:
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To simplify, we must try to find factors which are perfect squares. In this case 30 is a factor of 900 and is also a perfect square.
The square root of 
is equal to:
However,
Thus, 
To simplify, we must try to find factors which are perfect squares. In this case 30 is a factor of 900 and is also a perfect square.
The square root of
However,
Thus,
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Reduce.
Reduce.
Tap to reveal answer
To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 32 and is also a perfect square.
To reduce this expression, use the following steps:
To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 32 and is also a perfect square.
To reduce this expression, use the following steps:
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Find the square root of 
.
Find the square root of
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To simplify, we must try to find factors which are perfect squares. In this case 4 is a factor of 164 and is also a perfect square.
To find the square root of 
, use the following steps:
To simplify, we must try to find factors which are perfect squares. In this case 4 is a factor of 164 and is also a perfect square.
To find the square root of
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Reduce.
Reduce.
Tap to reveal answer
Use the following arithmetic steps to reduce 
.
To simplify, we must try to find factors which are perfect squares. In this case 64 is a factor of 192 and is also a perfect square.
Note 
and 
are both factors of 
, however only 
can be reduced.
Use the following arithmetic steps to reduce
To simplify, we must try to find factors which are perfect squares. In this case 64 is a factor of 192 and is also a perfect square.
Note
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Reduce.
Reduce.
Tap to reveal answer
To reduce this expression, first find factors of 
, then reduce.
To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 368 and is also a perfect square.
The solution is:
To reduce this expression, first find factors of
To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 368 and is also a perfect square.
The solution is:
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Find the square root of 
.
Find the square root of
Tap to reveal answer
To reduce this expression, first find factors of 
, then reduce.
To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 416 and is also a perfect square.
The solution is:
To reduce this expression, first find factors of
To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 416 and is also a perfect square.
The solution is:
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Simplify:
Simplify:
Tap to reveal answer
When simplifying the square root of a number that may not have a whole number root, it's helpful to approach the problem by finding common factors of the number inside the radicand. In this case, the number is 24,300.
What are the factors of 24,300?
24,300 can be factored into:
When there are factors that appear twice, they may be pulled out of the radicand. For instance, 100 is a multiple of 24,300. When 100 is further factored, it is (or 10x10). However, 100 wouldn't be pulled out of the radicand, but the square root of 100 because the square root of 24,300 is being taken. The 100 is part of the24,300. This means that the problem would be rewritten as:
But 243 can also be factored:
Following the same principle as for the 100, the problem would become
because there is only one factor of 3 left in the radicand. If there were another, the radicand would be lost and it would be 9*10*3.
9 and 10 may be multiplied together, yielding the final simplified answer of
When simplifying the square root of a number that may not have a whole number root, it's helpful to approach the problem by finding common factors of the number inside the radicand. In this case, the number is 24,300.
What are the factors of 24,300?
24,300 can be factored into:
When there are factors that appear twice, they may be pulled out of the radicand. For instance, 100 is a multiple of 24,300. When 100 is further factored, it is
But 243 can also be factored:
Following the same principle as for the 100, the problem would become
9 and 10 may be multiplied together, yielding the final simplified answer of
← Didn't Know|Knew It →
Tap to reveal answer
To solve the equation , we can first factor the numbers under the square roots.
When a factor appears twice, we can take it out of the square root.
Now the numbers can be added directly because the expressions under the square roots match.
To solve the equation
When a factor appears twice, we can take it out of the square root.
Now the numbers can be added directly because the expressions under the square roots match.
← Didn't Know|Knew It →
Simplify.
Simplify.
Tap to reveal answer
To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 624 and is also a perfect square.
Therefore we can rewrite the square root of 624 as:
To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 624 and is also a perfect square.
Therefore we can rewrite the square root of 624 as:
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Reduce to its simplest form.
Reduce
Tap to reveal answer
To simplify, we must try to find factors which are perfect squares. In this case 20 is a factor of 400 and is also a perfect square.
Thus we can rewrite the problem as:
Note:
To simplify, we must try to find factors which are perfect squares. In this case 20 is a factor of 400 and is also a perfect square.
Thus we can rewrite the problem as:
Note:
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Simplify.
Simplify.
Tap to reveal answer
Use the following steps to reduce this square root.
To simplify, we must try to find factors which are perfect squares. In this case 144 is a factor of 720 and is also a perfect square.
Thus we can rewrite the problem as follows.
Use the following steps to reduce this square root.
To simplify, we must try to find factors which are perfect squares. In this case 144 is a factor of 720 and is also a perfect square.
Thus we can rewrite the problem as follows.
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Find the square root of .
Find the square root of
Tap to reveal answer
Use the following steps to find the square root of
To simplify, we must try to find factors which are perfect squares. In this case 900 is a factor of 1800 and is also a perfect square.
Thus we can rewrite the problem as follows.
Use the following steps to find the square root of
To simplify, we must try to find factors which are perfect squares. In this case 900 is a factor of 1800 and is also a perfect square.
Thus we can rewrite the problem as follows.
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