Question

Blank radical 50 - 2 radical 8 = 6 radical blank

Answer 1

To simplify the expression \(\sqrt{50} - 2\sqrt{8}\) and find the value for the expression \(6\sqrt{\text{blank}}\), we can start by simplifying the radicals on the left-hand side.

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

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

3. Now we can substitute back into the original expression:
\[
\sqrt{50} - 2\sqrt{8} = 5\sqrt{2} - 4\sqrt{2} = (5 - 4)\sqrt{2} = 1\sqrt{2}
\]

Now we have simplified the left-hand side to \(\sqrt{2}\).

The equation we need to solve is:
\[
\sqrt{2} = 6\sqrt{\text{blank}}
\]

To isolate the radical, we divide both sides by 6:
\[
\sqrt{\text{blank}} = \frac{\sqrt{2}}{6}
\]

Now, we square both sides to find "blank":
\[
\text{blank} = \left(\frac{\sqrt{2}}{6}\right)^2 = \frac{2}{36} = \frac{1}{18}
\]

Thus, the value of "blank" is \(\frac{1}{18}\).