Algebra II : Square Roots

Example Questions

Simplify:

Explanation:

Rewrite the radical using common factors.

Recall that  is equivalent to the imaginary term .

Simplify the roots.

Evaluate:

Explanation:

Evaluate each square root.  The square root of the number is equal to a number multiplied by itself.

Example Question #11 : Square Roots

Explanation:

Simplify each radical.  A number inside the radical means that we are looking for a number times itself that will equal to that value inside the radical.

For a fourth root term, we are looking for a number that multiplies itself four times to get the number inside the radical.

Replace the values and determine the sum.

Explanation:

Do not multiply the terms inside the radical.  Instead, the terms inside the radical can be simplified term by term.

Simplify each square root.

Solve:

Explanation:

Solve by evaluating the square roots first.

Substitute the terms back into the expression.

Solve the square roots:

Explanation:

Evaluate each radical.  The square root of a certain number will output a number that will equal the term inside the radical when it's squared.

Replace all the terms.

Evaluate:

Explanation:

This expression is imaginary.  To simplify, we will need to factor out the imaginary term  as well as the perfect square.

Simplify the terms.

Solve:

Explanation:

Evaluate each square root.  The square root identifies a number that multiplies by itself to equal the number inside the square root.

Determine the sum.

Evaluate, if possible:

Explanation:

The negative numbers inside the radical indicates that we will have imaginary terms.

Recall that .

Rewrite the radicals using  as the common factor.

Replace the terms and evaluate the square roots.

Simplify: