# GED Math : Square Roots and Radicals

## Example Questions

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### Example Question #1 : Square Roots And Radicals

Simplify:

Explanation:

An alternate solution is:

Simplify:

Explanation:

Simplify:

Explanation:

Simplify:

Explanation:

Simplify:

Explanation:

### Example Question #1 : Square Roots And Radicals

Refer to the above number line. What point most likely represents the square root of 280?

Do not use a calculator.

Explanation:

Therefore,

making the correct choice .

### Example Question #2 : Square Roots And Radicals

Simplify:

Do not use a calculator.

The expression is in simplest form.

Explanation:

The prime factorization of 48 is

.

Rewrite, and use the product of radicals property to simplify:

### Example Question #8 : Square Roots And Radicals

Simplify:

Do not use a calculator.

The expression is in simplest form.

The expression is in simplest form.

Explanation:

The prime factorization of 42 is

.

Since 42 is the product of distinct primes, it has no perfect square factors, and, therefore, its square root cannot be simplified further. It is already in simplifed form.

### Example Question #9 : Square Roots And Radicals

Factor:

Explanation:

In order to factor the radical, we will need to rewrite 120 as multiples of perfect squares.

Reduce the known term

The value of  cannot be factored any further.

### Example Question #10 : Square Roots And Radicals

Factor:

Explanation:

Rewrite the root 40 in factors of perfect squares.