### All ACT Math Resources

## Example Questions

### Example Question #1 : Simplifying 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 #41 : Basic Squaring / Square Roots

Simplify .

**Possible Answers:**

**Correct answer:**

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

Therefore, .

### Example Question #21 : 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 #42 : Basic Squaring / Square Roots

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 #1 : 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 : Simplifying Square Roots

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 #1 : How To Simplify Square Roots

Which of the following is equal to ?

**Possible Answers:**

**Correct answer:**

When simplifying square roots, begin by prime factoring the number in question. For , this is:

Now, for each pair of numbers, you can remove that number from the square root. Thus, you can say:

Another way to think of this is to rewrite as . This can be simplified in the same manner.

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

Which of the following is equivalent to ?

**Possible Answers:**

**Correct answer:**

When simplifying square roots, begin by prime factoring the number in question. This is a bit harder for . Start by dividing out :

Now, is divisible by , so:

is a little bit harder, but it is also divisible by , so:

With some careful testing, you will see that

Thus, we can say:

Now, for each pair of numbers, you can remove that number from the square root. Thus, you can say:

Another way to think of this is to rewrite as . This can be simplified in the same manner.

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

What is the simplified (reduced) form of ?

**Possible Answers:**

It cannot be simplified further.

**Correct answer:**

To simplify a square root, you have to factor the number and look for pairs. Whenever there is a pair of factors (for example two twos), you pull one to the outside.

Thus when you factor 96 you get

### Example Question #1 : Simplifying Square Roots

Which of the following is equal to ?

**Possible Answers:**

**Correct answer:**

When simplifying square roots, begin by prime factoring the number in question. For , this is:

Now, for each pair of numbers, you can remove that number from the square root. Thus, you can say:

Another way to think of this is to rewrite as . This can be simplified in the same manner.