Solving Radical Equations Practice Problems

Solving Radical Equations Practice Problems-80
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Example We are to solve the following radical equation: $$\sqrt-x=0$$ First we isolate our radical: $$\sqrt=x$$ Then we square both sides and solve our equation: $$1 x^-x=x^$$ $$1-x=0$$ $$1=x$$ Lastly we plug our x into our original equation to check: $$\sqrt-1=0$$ $$\sqrt-1=0$$ $$1=1$$ The solution checks.

Solving radical equations requires applying the rules of exponents and following some basic algebraic principles.

This means that no value for a will result in a radical expression whose positive square root is −2!

You might have noticed that right away and concluded that there were no solutions for a.

A common method for solving radical equations is to raise both sides of an equation to whatever power will eliminate the radical sign from the equation.

But be careful—when both sides of an equation are raised to an even power, the possibility exists that extraneous solutions will be introduced.

Although x = −1 is shown as a solution in both graphs, squaring both sides of the equation had the effect of adding an extraneous solution, x = −6.

Again, this is why it is so important to check your answers when solving radical equations!

Take a look at this next problem that demonstrates a potential pitfall of squaring both sides to remove the radical..

Notice that the radical is set equal to −2, and recall that the principal square root of a number can only be positive.

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