8v+1= 4v+9 what is v when both are in square root

To solve the equation \( \sqrt{8v + 1} = \sqrt{4v + 9} \), we can start by squaring both sides to eliminate the square roots.

1. Square both sides:

\[
(\sqrt{8v + 1})^2 = (\sqrt{4v + 9})^2
\]

This simplifies to:

\[
8v + 1 = 4v + 9
\]

2. Now, solve for \( v \) by isolating it:

\[
8v - 4v = 9 - 1
\]

\[
4v = 8
\]

\[
v = \frac{8}{4} = 2
\]

So, the value of \( v \) is \( v = 2 \).

Would you like more details or have any questions? Here are 5 related questions:

1. How would the solution change if the equation was \( \sqrt{8v + 1} = \sqrt{4v + 9} + 2 \)?
2. What if the square root terms were multiplied by a coefficient?
3. How do you solve quadratic equations involving square roots?
4. Can you solve equations with multiple square roots on both sides?
5. How do you check if a solution to a square root equation is valid?

**Tip:** Always check your solutions by substituting them back into the original equation, especially when dealing with square roots, to avoid extraneous solutions.

Explore how to solve square root equations using an example problem. This equation involves isolating the variable under square roots, a fundamental concept in algebra. Suitable for high school students.

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