Solving an Equation Containing a Radical (2.9.2)

Question 1

• To solve an equation containing a radical, first eliminate the radical.

Answer 1

• To solve an equation containing a radical, first eliminate the radical.

Question 2

• If one side of the equation is nothing but a radical, squaring both sides instantly eliminates the radical. At the same time there will be significant changes on the other side of the equation.

Answer 2

• If one side of the equation is nothing but a radical, squaring both sides instantly eliminates the radical. At the same time there will be significant changes on the other side of the equation.

Question 3

• Extraneous roots do exist for these equations. Always check your answers to see which, if any, are really solutions for your equations.

Answer 3

• Extraneous roots do exist for these equations. Always check your answers to see which, if any, are really solutions for your equations.

Question 4

• Take only the principal (positive) square root when checking equations with radicals for extraneous roots.

Answer 4

• Take only the principal (positive) square root when checking equations with radicals for extraneous roots.

Question 5

The easiest way to eliminate a radical is to square both sides. You must square both sides to keep the equation balanced.

Now, move everything to the left side and set it equal to 0. Then, you’re ready to solve the equation. In this case,
factoring works.

Set each factor equal to 0, and solve for x. Now, you have
your two solutions.

Remember to check each solution to be sure it works.
Checking one answer, 3, we find that it works. So we have at least one solution; we know that x = 3.

One of your answers, –5, doesn’t work. So it is an extraneous root.

When you have some term(s) on the same side of the equation as the radical, your first step has to be to move them to the other side.

Once you have isolated your radical on its side of the
equation, then you do your squaring-both-sides trick. Now you are ready to solve.

Check both of your answers to see if both, only one, or neither is a solution for the original equation.

Once you have checked, you find you have one solution:
x = 3.
You have one extraneous root: x = 2.

Answer 5

The easiest way to eliminate a radical is to square both sides. You must square both sides to keep the equation balanced.

Now, move everything to the left side and set it equal to 0. Then, you’re ready to solve the equation. In this case,
factoring works.

Set each factor equal to 0, and solve for x. Now, you have
your two solutions.

Remember to check each solution to be sure it works.
Checking one answer, 3, we find that it works. So we have at least one solution; we know that x = 3.

One of your answers, –5, doesn’t work. So it is an extraneous root.

When you have some term(s) on the same side of the equation as the radical, your first step has to be to move them to the other side.

Once you have isolated your radical on its side of the
equation, then you do your squaring-both-sides trick. Now you are ready to solve.

Check both of your answers to see if both, only one, or neither is a solution for the original equation.

Once you have checked, you find you have one solution:
x = 3.
You have one extraneous root: x = 2.