Envision Math 2.0: Grade 8, Volume 1
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5. Solve Equations Using Square Roots and Cube Roots
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Exercise 12 Page 35

Take the square root of both sides of the equation.

y = ± 9

Practice makes perfect
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. y^2 = 81 Since y is raised to the second power, we will take the square root of both sides. Let's do it!
y^2=81
sqrt(y^2)=sqrt(81)

sqrt(a^2)=± a

y=± sqrt(81)
y=± 9