Exercise 4 Page 559

Practice makes perfect

a We are asked to solve the following square root equation.

5 = sqrt(x+20) To do so, let's recall the steps that we listed in the previous exercise.

Isolate the radical on one side of the equation.
Square both sides of the equation.
Solve the equation for the variable.
Substitute the solution into the original equation to check whether it is extraneous or not.

Since our radical is already isolated, we will continue by squaring both sides of the equation. Then, we will solve the equation for the variable x.

5= sqrt(x+20)

RaiseEqn

LHS^2=RHS^2

5^2=( sqrt(x+20))^2

CalcPow

Calculate power

25= x+20

SubEqn

LHS-20=RHS-20

5= x

RearrangeEqn

Rearrange equation

x=5

Great! Let's finally check the result by substituting x= 5 back into the original equation!

5=sqrt(x+20)

Substitute

x= 5

5 ? = sqrt(5+20)

AddTerms

Add terms

5 ? = sqrt(25)

CalcRoot

Calculate root

5 = 5 ✓

Since we found an identity, we know that the solution to the equation is x=5.

b We will solve the next square root equation by following the same steps that we took in Part A.

4 = sqrt(x-18)Having an isolated radical, we can immediately square both sides of the equation and then solve it for x.

4= sqrt(x-18)

RaiseEqn

LHS^2=RHS^2

4^2=( sqrt(x-18))^2

CalcPow

Calculate power

16= x-18

AddEqn

LHS+18=RHS+18

34= x

RearrangeEqn

Rearrange equation

x=34

At last, we will substitute the solution back into the original equation to check the extraneous solutions.

4=sqrt(x-18)

Substitute

x= 34

4 ? = sqrt(34-18)

SubTerms

Subtract terms

4 ? = sqrt(16)

CalcRoot

Calculate root

4 = 4 ✓

Great! We ended with an identity again. Therefore, the result is x=34.

c Let's take a look at the given equation.

sqrt(x)+2 = 3One more time, we will solve it by applying the same steps as listed in Part A. This time, we will first isolate the radical on one side and then square both sides of the equation. Let's do it!

sqrt(x)+2=3

SubEqn

LHS-2=RHS-2

sqrt(x)=1

RaiseEqn

LHS^2=RHS^2

( sqrt(x))^2=1^2

CalcPow

Calculate power

x=1

Now, we will check the result.

sqrt(x)+2=3