### All SAT Math Resources

## Example Questions

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

Simplify .

**Possible Answers:**

**Correct answer:**

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

Simplfy the following radical .

**Possible Answers:**

**Correct answer:**

You can rewrite the equation as .

This simplifies to .

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

Which of the following is equal to ?

**Possible Answers:**

**Correct answer:**

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

### Example Question #111 : Arithmetic

Simplify .

**Possible Answers:**

**Correct answer:**

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

Therefore, .

### Example Question #112 : Arithmetic

What is ?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

First find all of the prime factors of

So

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

What is equal to?

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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.

The answer is:

### Example Question #11 : Simplifying Square Roots

Simplify:

**Possible Answers:**

None of the given answers.

**Correct answer:**

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: