Algebra II : Solving and Graphing Radicals

Example Questions

Example Question #71 : Solving And Graphing Radicals

Solve the equation:

Explanation:

Cube both sides of the equation.

This will eliminate the radical on the left side.

Divide by three on both sides.  This is similar to multiplying one-third on both sides.

Example Question #72 : Solving And Graphing Radicals

Explanation:

Subtract both sides by three.

The equation becomes:

Divide both sides by negative one.

Cube both sides to eliminate the radical.

Subtract 64 on both sides.

Example Question #73 : Solving And Graphing Radicals

Explanation:

Raise both sides by the power of eight to eliminate the radical.

Simplify both sides.

Divide by two on both sides.

Example Question #74 : Solving And Graphing Radicals

Solve:

Explanation:

Multiply by  on both sides.

Divide by 4 on both sides.

Square both sides to eliminate the radical.

Divide by three on both sides.  This is similar to multiplying both sides by one third.

Example Question #75 : Solving And Graphing Radicals

Solve:

Explanation:

Multiply both sides by the denominator on the left side.

The equation becomes:

Square both sides to eliminate the radical.

Divide both sides by eight.

Notice that the negative radical solution will not satisfy the original equation.

Rationalize the positive term.

Example Question #76 : Solving And Graphing Radicals

Solve:

Explanation:

Raise both sides to the power of four.

Simplify both sides.

Subtract 1 from both sides.

Divide by 32 on both sides.

Reduce this fraction.

Example Question #77 : Solving And Graphing Radicals

Solve the equation:

Explanation:

In order to eliminate the radical on both sides, we will need to cube both sides.

Simplify both sides.

Divide by eight on both sides.

Reduce the fractions on both sides.

Example Question #78 : Solving And Graphing Radicals

Solve:

Explanation:

Square both sides to eliminate the radical.

Subtract three on both sides.

The equation becomes:

Divide by negative five on both sides.

Example Question #79 : Solving And Graphing Radicals

Solve the equation:

Explanation:

Subtract eight from both sides.

Raise both sides by the power of four.

Divide both sides by three.

Solve:

Explanation: