7 fraction 4 root of 2 dot fourth root of two over fourth root of two

Answer 1

To simplify the expression \(\frac{7 \frac{4\sqrt{2} \cdot \sqrt[4]{2}}{\sqrt[4]{2}}}{1}\), follow these steps:

1. Simplify the fraction: \(\frac{4\sqrt{2} \cdot \sqrt[4]{2}}{\sqrt[4]{2}}\).

Since \(\sqrt[4]{2}\) in the numerator and denominator cancels out, we have:

\[ 4\sqrt{2}. \]

2. Combine with 7: Now you're left with:

\[ 7 \cdot 4\sqrt{2} = 28\sqrt{2}. \]

Therefore, the simplified form of the original expression is:

\[ 28\sqrt{2}. \]