Questions: Question 7 (Multiple Choice Worth 2 points) (Solving Equations Using Square and Cube Roots LC) Solve y^3 = -125 y = -5 y = ± 5 y = -25 y = ± 25

Transcript text: Question 7 (Multiple Choice Worth 2 points) (Solving Equations Using Square and Cube Roots LC) Solve $y^{3}=-125$ $y=-5$ $y= \pm 5$ $y=-25$ $y= \pm 25$

Solution

Solution Steps

To solve the equation $ y^3 = -125 $, we need to find the cube root of $-125$. The cube root of a negative number is also negative, and since $ (-5)^3 = -125 $, the solution is $ y = -5 $.

Step 1: Solve the Equation

We start with the equation $ y^3 = -125 $. To find $ y $, we take the cube root of both sides:

\[ y = \sqrt[3]{-125} \]

Step 2: Calculate the Cube Root

The cube root of $-125$ can be expressed as:

\[ y = -5 \]

This is because $ (-5)^3 = -125 $.

Step 3: Verify the Solution

To verify, we can substitute $ y = -5 $ back into the original equation:

\[ (-5)^3 = -125 \]

This confirms that our solution is correct.