# SAT Math : Arithmetic

## Example Questions

Simplify .

Explanation:

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

Simplfy the following radical .

Explanation:

You can rewrite the equation as .

This simplifies to .

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

Which of the following is equal to  ?

Explanation:

√75 can be broken down to √25 * √3. Which simplifies to 5√3.

### Example Question #111 : Arithmetic

Simplify .

Explanation:

Rewrite what is under the radical in terms of perfect squares:

Therefore, .

### Example Question #112 : Arithmetic

What is ?

Explanation:

We know that 25 is a factor of 50. The square root of 25 is 5. That leaves  which can not be simplified further.

### Example Question #113 : Arithmetic

Which of the following is equivalent to ?

Explanation:

Multiply by the conjugate and the use the formula for the difference of two squares:

### Example Question #14 : Simplifying Square Roots

Which of the following is the most simplified form of:

Explanation:

First find all of the prime factors of

So

### Example Question #2 : Properties Of Roots And Exponents

What is  equal to?

Explanation:

1. We know that , which we can separate under the square root:

2. 144 can be taken out since it is a perfect square: . This leaves us with:

This cannot be simplified any further.

### Example Question #111 : Arithmetic

Simplify:

Explanation:

Write out the common square factors of the number inside the square root.

Continue to find the common factors for 60.

Since there are no square factors for , the answer is in its simplified form.  It might not have been easy to see that 16 was a common factor of 240.

### Example Question #11 : Simplifying Square Roots

Simplify:

None of the given answers.

Explanation:

To simplify, we want to find some factors of  where at least one of the factors is a perfect square.

In this case,  and  are factors of , and  is a perfect square.

We can simplify by saying:

We could also recognize that two factors of  are  and . We could approach this way by saying:

But we wouldn't stop there. That's because  can be further factored: