# PSAT Math : How to find a rational number from an exponent

## Example Questions

Explanation:

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

Rationalize the denominator:

Explanation:

The conjugate of is  .

Now multiply both the numerator and the denominator by

and you get:

Hence we get

Solve for :

Explanation:

Solve for .

Explanation:

If,

What does

Explanation:

If  ,

then .

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

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.

### Example Question #7 : How To Find A Rational Number From An Exponent

For some positive integer , if , what is the value of ?

Explanation:

If , then  must equal 3 (Note that  cannot be -3 because you need it to be positive.

Now, plug  into the new equation :