### All SAT Math Resources

## Example Questions

### Example Question #1 : How To Find A Rational Number From An Exponent

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #2 : How To Find A Rational Number From An Exponent

Rationalize the denominator:

**Possible Answers:**

**Correct answer:**

Explanation:

The conjugate of is .

Now multiply both the numerator and the denominator by

and you get:

Hence we get

### Example Question #3 : How To Find A Rational Number From An Exponent

Solve for :

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #4 : How To Find A Rational Number From An Exponent

Solve for .

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #5 : How To Find A Rational Number From An Exponent

If,

What does

**Possible Answers:**

**Correct answer:**

Explanation:

If ,

then .

### Example Question #6 : How To Find A Rational Number From An Exponent

**Possible Answers:**

**Correct answer:**

Explanation:

From the equation in the problem statement

Now squaring both sides we get

this is a quadratic equation which equals

and the factors of this equation are

This gives us .

However, if we plug these solutions back into the original equation, does not create an equality. Therefore, is an extraneous solution.

Patrick

Certified Tutor

Certified Tutor

University of North Texas, Bachelors, Mathematics. Texas A & M University-Commerce, Current Grad Student, Mathematics.