Questions: Solve y^2=64, where y is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". y=

Solve y^2=64, where y is a real number.
Simplify your answer as much as possible.
If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".
y=

Transcript text: Solve $y^{2}=64$, where $y$ is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". \[ y= \]

Solution

Solution Steps

To solve the equation $ y^2 = 64 $, we need to find the real numbers $ y $ such that when squared, they equal 64. This involves taking the square root of both sides of the equation. Since both positive and negative numbers can square to give a positive result, we should consider both the positive and negative square roots of 64.

Step 1: Identify the Equation

We start with the equation $ y^2 = 64 $. Our goal is to find the values of $ y $ that satisfy this equation.

Step 2: Solve for $ y $

To solve for $ y $, we take the square root of both sides of the equation. This gives us two possible solutions because both a positive and a negative number can square to give a positive result.

\[ y = \pm \sqrt{64} \]

Step 3: Calculate the Square Roots

Calculate the square root of 64:

\[ \sqrt{64} = 8 \]

Thus, the solutions are:

\[ y = 8 \quad \text{and} \quad y = -8 \]