Question

Blank radical 50 - 2 radical 8 = 6 radical

Answer 1

To simplify the expression \( \sqrt{50} - 2\sqrt{8} \) and determine the value of the unknown radical, we will first simplify each radical.

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

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

Now we can subtract:
\[
\sqrt{50} - 2\sqrt{8} = 5\sqrt{2} - 4\sqrt{2} = (5 - 4)\sqrt{2} = 1\sqrt{2} = \sqrt{2}.
\]

From the equation given:
\[
\sqrt{50} - 2\sqrt{8} = 6\sqrt{x}.
\]
We have found that the left side simplifies to \( \sqrt{2} \):
\[
\sqrt{2} = 6\sqrt{x}.
\]

To solve for \( x \), we divide both sides by 6:
\[
\sqrt{x} = \frac{\sqrt{2}}{6}.
\]

Now, squaring both sides:
\[
x = \left(\frac{\sqrt{2}}{6}\right)^2 = \frac{2}{36} = \frac{1}{18}.
\]

Thus, the value of the unknown radical \( x \) is:
\[
\boxed{\frac{1}{18}}.
\]