# High School Math : Simplifying Radicals

## Example Questions

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### Example Question #1 : Simplifying Radicals

Factor and simplify the following radical expression:

Explanation:

Begin by factoring the integer:

Now, simplify the exponents:

### Example Question #1 : Simplifying Radicals

Factor and simplify the following radical expression:

Explanation:

Begin by converting the radical into exponent form:

Now, multiply the exponents:

### Example Question #3 : Simplifying Radicals

Factor and simplify the following radical expression:

Explanation:

Begin by converting the radical into exponent form:

Now, combine the bases:

Simplify the integer:

Now, simplify the exponents:

Convert back into radical form and simplify:

### Example Question #4 : Simplifying Radicals

Factor and simplify the following radical expression:

Explanation:

Begin by multiplying the numerator and denominator by the complement of the denominator:

Use the FOIL method to multiply the radicals. F (first) O (outer) I (inner) L (last)

Now, combine like terms:

Simplify:

### Example Question #5 : Simplifying Radicals

Factor and simplify the following radical expression:

Explanation:

Combine like terms:

Multiply the left side by  and the right side by

### Example Question #6 : Simplifying Radicals

Factor and simplify the following radical expression:

Explanation:

Begin by converting the radicals into exponent form:

Now, combine the bases:

Convert back into radical form and simplify:

### Example Question #7 : Simplifying Radicals

Factor and simplify the following radical expression:

Explanation:

Begin by simplifying the right side of the rational expression:

Now, combine like terms:

### Example Question #8 : Simplifying Radicals

Factor and simplify the following radical expression:

Explanation:

Begin by using the FOIL method to multiply the radical expression. F (first) O (outer) I (inner) L (last)

Now, combine like terms:

### Example Question #9 : Simplifying Radicals

Factor and simplify the following radical expression:

Explanation:

Begin by multiplying the numerator and denominator by :

The expression cannot be further simplified.

### Example Question #10 : Simplifying Radicals

Factor and simplify the following radical expression: