# SAT Math : Arithmetic

## Example Questions

### Example Question #14 : Square Roots And Operations

Simplify:

Explanation:

To simplify the problem, just distribute the radical to each term in the parentheses.

### Example Question #15 : Square Roots And Operations

Simplify:

Explanation:

Let's simplify the right parentheses.

Now we can distribute the radical to each term in the parentheses.

### Example Question #16 : Square Roots And Operations

If  what is ?

Explanation:

Square both sides:

x = (32)2 = 92 = 81

### Example Question #17 : Square Roots And Operations

Simplify in radical form:

Explanation:

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 #36 : Arithmetic

Simplify:

None of the other answers

Explanation:

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 #31 : Basic Squaring / Square Roots

Simplify the following expression:

Explanation:

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 #1 : How To Add Square Roots

Solve for .

Note, :

Explanation:

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 :

### Example Question #179 : Arithmetic

Evaluate:

None of the available answers

Explanation:

Let us factor 108 and 81

### Example Question #1 : Basic Squaring / Square Roots

(√27 + √12) / √3 is equal to

5

(6√3)/√3

5/√3

18

√3

5

Explanation:

√27 is the same as 3√3, while √12 is the same as 2√3.

3√3 + 2√3 = 5√3

(5√3)/(√3) = 5

Simplify: