***Square root is by itself on one side of eq.**

If you square a square root, it will disappear. This is what
we want to do here so that we can get *x* out
from under the square root and continue to solve for it.

No more radicals exist, so we do not have to repeat steps 1 and 2.

In this example, the equation that resulted from squaring both sides
turned out to be a **linear equation**.

If you need a review on solving linear equations, feel free to go to **Tutorial
14: Linear Equations in One Variable**.

***False statement**

**There is no solution to this radical equation.**

The radical in this equation is already isolated.

If you square a square root, it will disappear. This is what
we want to do here so that we can get *y* out
from under the square root and continue to solve for it.

***Right side is a binomial
squared**

***Square root is by itself on one side of eq.**

***Inverse of taking the sq. root is squaring
it**

***Left side is a binomial
squared**

In this example, the equation that resulted from squaring both sides
turned out to be a **quadratic** **equation**.

If you need a review on solving quadratic equations feel free to go
to **Tutorial 17: Quadratic Equations.**

***Quad. eq. in standard form**

***Factor
out a GCF of 4**

***Factor
the trinomial**

***Use Zero-Product
Principle**

***Set 1st factor = 0 and solve**

***Set 2nd factor = 0 and solve**

***True statement**

***True statement**

**There are two solutions to this radical equation: x = 3 and x = -1.**

***Inverse of mult. by 3 is div. by 3**

***rat. exp. expression is by itself on one side
of eq.**

If you raise an expression that has a rational exponent to the reciprocal
of that rational exponent, the exponent will disappear. This
is what we want to do here so that we can get *x* out from under the rational exponent and continue to solve for it.

In this example, the equation that resulted from raising both sides
to the 2/5 power turned out to be a **linear equation**.

Also note that it is already solved for *x*.
So, we do not have to do anything on this step for this example.

***Plugging in 3 to the 2/5 power for x**

***True statement**

**There is one solution to this rational exponent equation: .**

The base with the rational exponent is already isolated.

If you raise an expression that has a rational exponent to the reciprocal
of that rational exponent, the exponent will disappear. This
is what we want to do here so that we can get *x* out from under the rational exponent and continue to solve for it.

***Use def.
of rat. exp**

In this example, the equation that resulted from squaring both sides
turned out to be a **quadratic** **equation**.

If you need a review on solving quadratic equations, feel free to go
to **Tutorial 17: Quadratic Equations.**

***Quad. eq. in standard form**

***Factor
the trinomial**

***Use Zero-Product
Principle**

***Set 1st factor = 0 and solve**

***Set 2nd factor = 0 and solve**

***Plugging in -6 for x**

***True statement**

***True statement**

**There are two solutions to this rational exponent equation: x = -6 and x = -3.**

Last revised on Dec. 16, 2009 by Kim Seward.

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