### All SAT Math Resources

## Example Questions

### Example Question #21 : Basic Squaring / Square Roots

If what is ?

**Possible Answers:**

**Correct answer:**

Square both sides:

x = (3^{2})^{2}^{ }= 9^{2} = 81

### Example Question #2 : How To Add Square Roots

Simplify in radical form:

**Possible Answers:**

**Correct answer:**

To simplify, break down each square root into its component factors:

You can remove pairs of factors and bring them outside the square root sign. At this point, since each term shares , you can add them together to yield the final answer:

### Example Question #1 : How To Add Square Roots

Simplify:

**Possible Answers:**

None of the other answers

**Correct answer:**

Take each fraction separately first:

(2√3)/(√2) = [(2√3)/(√2)] * [(√2)/(√2)] = (2 * √3 * √2)/(√2 * √2) = (2 * √6)/2 = √6

Similarly:

(4√2)/(√3) = [(4√2)/(√3)] * [(√3)/(√3)] = (4√6)/3 = (4/3)√6

Now, add them together:

√6 + (4/3)√6 = (3/3)√6 + (4/3)√6 = (7/3)√6

### Example Question #3 : Square Roots And Operations

Simplify the following expression:

**Possible Answers:**

**Correct answer:**

Begin by factoring out each of the radicals:

For the first two radicals, you can factor out a or :

The other root values cannot be simply broken down. Now, combine the factors with :

This is your simplest form.

### Example Question #4 : Square Roots And Operations

Solve for .

Note, :

**Possible Answers:**

**Correct answer:**

Begin by getting your terms onto the left side of the equation and your numeric values onto the right side of the equation:

Next, you can combine your radicals. You do this merely by subtracting their respective coefficients:

Now, square both sides:

Solve by dividing both sides by :