Question

Blank radical 50 - 2 radical 8 = 6 radical BL

Answer 1

To solve the equation \( \sqrt{50} - 2\sqrt{8} = 6\sqrt{BL} \), we will first simplify the left side.

1. **Simplifying \(\sqrt{50}\)**:
\[
\sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}
\]

2. **Simplifying \(2\sqrt{8}\)**:
\[
\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}
\]
So,
\[
2\sqrt{8} = 2 \cdot 2\sqrt{2} = 4\sqrt{2}
\]

3. **Combining the terms on the left side**:
Now substitute back into the equation:
\[
5\sqrt{2} - 4\sqrt{2} = (5 - 4)\sqrt{2} = 1\sqrt{2} = \sqrt{2}
\]

Now we have:
\[
\sqrt{2} = 6\sqrt{BL}
\]

4. **Dividing both sides by 6**:
\[
\sqrt{BL} = \frac{\sqrt{2}}{6}
\]

5. **Squaring both sides**:
\[
BL = \left(\frac{\sqrt{2}}{6}\right)^2 = \frac{2}{36} = \frac{1}{18}
\]

Therefore, \( BL = \frac{1}{18} \).