# College Algebra : Review and Other Topics

## Example Questions

### Example Question #331 : College Algebra

Which of the following is equal to ?

Explanation:

Factor the radical by values of perfect squares.

Replace the term.

### Example Question #61 : Review And Other Topics

Explanation:

Square both sides to eliminate the radical.

Solve for x.  Subtract two on both sides.

### Example Question #11 : Radicals

What is the value of ?

Explanation:

Multiply all numbers to combine the radicals.

Factor this value using numbers of perfect squares.

### Example Question #16 : Radicals

Explanation:

In order to multiply radicals, first rewrite the problem as follows:

This follows a basic property of radical multiplication.

Since 100 is a perfect square the final answer to the problem is 10.

### Example Question #17 : Radicals

Explanation:

In order to multiply radicals, first rewrite the problem as follows:

This follows a basic property of radical multiplication.

Although 20 is not a perfect square, one of its factors is. We can break the radical up and simplify as follows:

This gives us a final answer of

### Example Question #12 : Radicals

Explanation:

In order to multiply radicals, first rewrite the problem as follows:

This follows a basic property of radical multiplication.

Although 45 is not a perfect square, one of its factors is. We can break the radical up and simplify as follows:

This gives us a final answer of

### Example Question #13 : Radicals

Explanation:

In order to multiply radicals, first rewrite the problem as follows:

This follows a basic property of radical multiplication.

Although 12 is not a perfect square, one of its factors is. We can break the radical up and simplify as follows:

This gives us a final answer of

### Example Question #11 : Radicals

Explanation:

In order to multiply radicals, first rewrite the problem as follows:

This follows a basic property of radical multiplication.

Since 36 is a perfect square the final answer to the problem is 6.

### Example Question #21 : Radicals

Explanation:

This set of radicals can be considered a special case.

Because 4 is a perfect square and 6 cannot be simplified any further, solve by taking the square root of 4:

This means the final answer is

### Example Question #22 : Radicals

Explanation:

In order to add or subtract, first simplify each radical completely. If the remaining number under the square root sign is the same for both numbers they can be added- much like with variables.

For this problem, it goes as follows:

Both radicals are completely simplified, but their bases are not the same. This means we get a final answer of