Question

Simplify the expression by subtracting the radicals blank radical 50 - 2 radical 8 = 6 radical blank

Answer 1

To simplify the expression \( \sqrt{50} - 2\sqrt{8} \) and express it in the form \( 6\sqrt{x} \), we need to simplify each of the radicals.

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

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

Therefore:
\[
2\sqrt{8} = 2 \cdot 2\sqrt{2} = 4\sqrt{2}
\]

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

Thus, the expression simplifies to:
\[
\sqrt{2}
\]

To express \( \sqrt{2} \) in the form \( 6\sqrt{x} \), we see that:
\[
1\sqrt{2} = 6\sqrt{\frac{2}{36}} = 6\sqrt{\frac{1}{18}} = 6\sqrt{2}\times \frac{1}{6}
\]
So, if we set \( 6\sqrt{x} = \sqrt{2} \), we must have \( x = \frac{1}{36} \).

Consequently, the original requested expression can be stated as:
\[
\sqrt{50} - 2\sqrt{8} = 6\sqrt{\frac{1}{36}}
\]

Thus, filling in the blanks:
\[
\sqrt{50} - 2\sqrt{8} = 6\sqrt{2}, \text{, (so x = 2)}
\]
The final answer is:
- The value for \( x \) is \( 2 \).