How to multiply square roots - GRE Quantitative Reasoning
Card 0 of 4
Solve for 
:
Solve for
You can "break apart" the fractional square root:
into:
Therefore, you can rewrite your equation as:
Now, multiply both sides by 
:
Now, you can square both sides of your equation and get:
You can "break apart" the fractional square root:
into:
Therefore, you can rewrite your equation as:
Now, multiply both sides by
Now, you can square both sides of your equation and get:
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Begin by multiplying what is under the square roots together. Remember:
Therefore:
We must now try to reduce the square root. Look for factors that can be taken out that can be easily square-rooted. It's a good idea to start with small square roots 
. In this case, we can factor out a 9 from 135:
Now take the square root of 9, and we are left with our answer:
Begin by multiplying what is under the square roots together. Remember:
Therefore:
We must now try to reduce the square root. Look for factors that can be taken out that can be easily square-rooted. It's a good idea to start with small square roots
Now take the square root of 9, and we are left with our answer:
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The length of a square courtyard is 
feet.
What is the area of the courtyard?
The length of a square courtyard is
What is the area of the courtyard?
The area of a square is length squared. In this case, that would be 
which is equivalent to 
. At this point, you multiply the values underneath the square root, then simplify:
.
The square root of a base squared is then just the base:
Lastly, we apply the appropriate units, therefore the area of the courtyard is 
.
The area of a square is length squared. In this case, that would be
The square root of a base squared is then just the base:
Lastly, we apply the appropriate units, therefore the area of the courtyard is
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Solve:
Solve:
To solve this problem, we must know how to multiply/divide with square roots. The rules involved are quite simple. When multiplying square roots together, multiply the coeffcients of the two numbers together and then multiply the two radicands together. The product of the radicand becomes the new radicand and the product of the coeffcients become the new coeffcient. The radicand is simply the number within the square root.
Dividing square roots follows the exact same rules as multiplying square roots, divide the coeffcients together, the result is the coeffcient for final answer. Do the same for the radicands.
To solve this problem, we must know how to multiply/divide with square roots. The rules involved are quite simple. When multiplying square roots together, multiply the coeffcients of the two numbers together and then multiply the two radicands together. The product of the radicand becomes the new radicand and the product of the coeffcients become the new coeffcient. The radicand is simply the number within the square root.
Dividing square roots follows the exact same rules as multiplying square roots, divide the coeffcients together, the result is the coeffcient for final answer. Do the same for the radicands.
Compare your answer with the correct one above