GRE Math : How to multiply square roots

Example Questions

Example Question #51 : Arithmetic

Solve for :

Explanation:

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:

Example Question #51 : Arithmetic

The length of a square courtyard is  feet.

What is the area of the courtyard?

Explanation:

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 .

Example Question #56 : Basic Squaring / Square Roots

Explanation:

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:

Solve: