Exercise 33 Page 262

Each time we solve a radical equation, we begin by isolating the radical term on one side of the equation. In the first of the given equations, we need to subtract 1 from both sides of the equation to isolate sqrt(x). 5 &=sqrt(x)+1 5 - 1 &= sqrt(x)+1 - 1 4 &=sqrt(x) Then, to solve the equation completely, we raise both sides of the equation to the second power.

4=sqrt(x)

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LHS^2=RHS^2

RaiseEqn

LHS^2=RHS^2

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

CalcPow

Calculate power

16=x

RearrangeEqn

Rearrange equation

x=16

In the second of the given equations, the radical term is already isolated. This time, our first step is different than it was before. Here, we begin by raising both sides of the equation to the second power. 5 &= sqrt(x+1) 5^2 &= (sqrt(x+1))^2 25 &= x+1 Now we will isolate x by subtracting.

25=x+1

SubEqn

LHS-1=RHS-1

24=x

RearrangeEqn

Rearrange equation

x=24

As we can see, the main difference in solving these two equations was the order of the steps that we needed to take.

	First Step	Second Step
5=sqrt(x)+1	Subtract to isolate the radical	Square both sides to remove the radical
5=sqrt(x+1)	Square both sides to remove the radical	Subtract to isolate x