Square Roots and Operations - GRE Quantitative Reasoning

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:

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:

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 .

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.

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:

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:

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 .

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.

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:

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:

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 .

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.

Begin by breaking down each of the roots in question. Often, for the GRE, your answer arises out of doing such basic "simplification moves".

Quantity A

This is the same as:

, which can be reduced to:

Quantity B

This is the same as:

, which can be reduced to:

Now, since we know that must be greater than , we know that . Therefore, quantity A is larger.

Begin by subtracting from both sides:

This simplifies to:

Now, while you could square both sides, you also know that merely needs to be the same as the value under the other radical. This means that it is —simply and quickly! (Always work to save time on the exam!)

As always for comparison questions, work on getting your quantities explicit. In order to do this in this case, you must factor the roots.

Quantity A

This can be factored into:

Quantity B

This can be factored into:

This makes the comparison very easy! Since is a larger number than , we know that is a smaller value than . Therefore, Quantity B is larger.

Begin by breaking down each of the roots in question. Often, for the GRE, your answer arises out of doing such basic "simplification moves".

Quantity A

This is the same as:

, which can be reduced to:

Quantity B

This is the same as:

, which can be reduced to:

Now, since we know that must be greater than , we know that . Therefore, quantity A is larger.

Begin by subtracting from both sides:

This simplifies to:

Now, while you could square both sides, you also know that merely needs to be the same as the value under the other radical. This means that it is —simply and quickly! (Always work to save time on the exam!)

As always for comparison questions, work on getting your quantities explicit. In order to do this in this case, you must factor the roots.

Quantity A

This can be factored into:

Quantity B

This can be factored into:

This makes the comparison very easy! Since is a larger number than , we know that is a smaller value than . Therefore, Quantity B is larger.

Begin by breaking down each of the roots in question. Often, for the GRE, your answer arises out of doing such basic "simplification moves".

Quantity A

This is the same as:

, which can be reduced to:

Quantity B

This is the same as:

, which can be reduced to:

Now, since we know that must be greater than , we know that . Therefore, quantity A is larger.

Begin by subtracting from both sides:

This simplifies to:

Now, while you could square both sides, you also know that merely needs to be the same as the value under the other radical. This means that it is —simply and quickly! (Always work to save time on the exam!)