Exercise 3 Page 386

Let's start by recalling how to solve equations that contain a variable that is squared and equal to a non-negative number. These types of equations have two solutions. x^2=a ⇒ x=± sqrt(a) This is because both (sqrt(a))^2 and (- sqrt(a))^2 are equal to a. Let's think of a more concrete example. sqrt(9)=±3 because 3^2=9 and (-3)^2=9 With this in mind, let's solve the given equation. sqrt(1000/10)=n^2-54 First, we need to isolate the variable term on one side of the equation and simplify the square root. To do so, we will use the Properties of Equality.

sqrt(1000/10)=n^2-54

CalcQuot

Calculate quotient

sqrt(100)=n^2-54

CalcRoot

Calculate root

10=n^2-54

AddEqn

LHS+54=RHS+54

10+54=n^2-54+54

AddTerms

Add terms

64=n^2

RearrangeEqn

Rearrange equation

n^2=64

Next, since n is raised to the second power, we will take the square root of both sides. Let's do it!

n^2=64

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(n^2)=sqrt(64)

sqrt(a^2)=± a

n=± sqrt(64)

CalcRoot

Calculate root

n=± 8

The solutions are n=-8 and n=8.