Square root of b squared -10 squared =15

1 answer

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: \[ b = 5\sqrt{13} \quad \text{or} \quad b = -5\sqrt{13} \]