### All PSAT Math Resources

## Example Questions

### Example Question #2 : How To Factor A Common Factor Out Of Squares

Simplify the expression.

**Possible Answers:**

**Correct answer:**

Use the distributive property for radicals.

Multiply all terms by .

Combine terms under radicals.

Look for perfect square factors under each radical. has a perfect square of . The can be factored out.

Since both radicals are the same, we can add them.

### Example Question #1 : Complex Numbers

Simplify by rationalizing the denominator:

**Possible Answers:**

**Correct answer:**

Multiply both numerator and denominator by :

### Example Question #2 : Complex Numbers

Divide:

**Possible Answers:**

**Correct answer:**

Rewrite in fraction form, and multiply both numerator and denominator by :

### Example Question #1 : Complex Numbers

Simplify by rationalizing the denominator:

**Possible Answers:**

**Correct answer:**

Multiply both numerator and denominator by :

### Example Question #1 : Complex Numbers

Simplify by rationalizing the denominator:

**Possible Answers:**

**Correct answer:**

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is :

### Example Question #1 : How To Divide Complex Numbers

Simplify by rationalizing the denominator:

**Possible Answers:**

**Correct answer:**

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is :

### Example Question #2 : Complex Numbers

Simplify by rationalizing the denominator:

**Possible Answers:**

**Correct answer:**

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is :

### Example Question #7 : Complex Numbers

Define an operation as follows:

For all complex numbers ,

.

Evaluate .

**Possible Answers:**

**Correct answer:**

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is . The above becomes:

### Example Question #2 : How To Divide Complex Numbers

Define an operation as follows:

For all complex numbers ,

.

Evaluate .

**Possible Answers:**

**Correct answer:**

### Example Question #9 : Complex Numbers

Define an operation as follows:

For all complex numbers ,

Evaluate .

**Possible Answers:**

**Correct answer:**

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is . The above becomes:

Certified Tutor