Question

Square root of b squared -10 squared =15

Answer 1

To solve the equation \( \sqrt{b^2 - 10^2} = 15 \), we will first isolate the square root and then square both sides to eliminate it.

1. Start with the equation:
\[
\sqrt{b^2 - 10^2} = 15
\]

2. Square both sides:
\[
b^2 - 10^2 = 15^2
\]
This simplifies to:
\[
b^2 - 100 = 225
\]

3. Add 100 to both sides:
\[
b^2 = 225 + 100
\]
\[
b^2 = 325
\]

4. Take the square root of both sides:
\[
b = \pm \sqrt{325}
\]

5. Simplify \( \sqrt{325} \):
\[
\sqrt{325} = \sqrt{25 \times 13} = \sqrt{25} \times \sqrt{13} = 5\sqrt{13}
\]

So, the solutions for \( b \) are:
\[
b = 5\sqrt{13} \quad \text{or} \quad b = -5\sqrt{13}
\]