Question

solve ( v^2 = 25 ), where ( v ) 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
o solution\.

Explanation:

Step 1: Identify the equation

The equation given is \( v^2 = 25 \). We need to solve for \( v \) where \( v \) is a real number.

Step 2: Use the square root property

To solve for \( v \), we can take the square root of both sides of the equation. Remember that if \( x^2 = a \) (where \( a\geq0 \)), then \( x=\pm\sqrt{a} \).

Applying this property to our equation \( v^2 = 25 \), we take the square root of both sides:

\( v=\pm\sqrt{25} \)

Step 3: Simplify the square root

We know that \( \sqrt{25} = 5 \) because \( 5\times5 = 25 \) and \( (- 5)\times(-5)=25 \). So,

\( v=\pm5 \)

The solutions to the equation \( v^2 = 25 \) are \( v = 5 \) and \( v=- 5 \). So the answer is \( 5, - 5 \).

Answer:

Step 1: Identify the equation

The equation given is \( v^2 = 25 \). We need to solve for \( v \) where \( v \) is a real number.

Step 2: Use the square root property

To solve for \( v \), we can take the square root of both sides of the equation. Remember that if \( x^2 = a \) (where \( a\geq0 \)), then \( x=\pm\sqrt{a} \).

Applying this property to our equation \( v^2 = 25 \), we take the square root of both sides:

\( v=\pm\sqrt{25} \)

Step 3: Simplify the square root

We know that \( \sqrt{25} = 5 \) because \( 5\times5 = 25 \) and \( (- 5)\times(-5)=25 \). So,

\( v=\pm5 \)

The solutions to the equation \( v^2 = 25 \) are \( v = 5 \) and \( v=- 5 \). So the answer is \( 5, - 5 \).