If \(\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}\), find K
Question 1 Report
If \(\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}\), find K
Answer Details
We can start by simplifying the left-hand side of the equation using the laws of square roots:
\begin{align*}
\sqrt{50} - K\sqrt{8} &= \sqrt{25\cdot 2} - K\sqrt{4\cdot 2} \\
&= 5\sqrt{2} - 2K\sqrt{2} \\
&= \sqrt{2}(5 - 2K).
\end{align*}
Now, we can rewrite the given equation as:
\begin{align*}
\sqrt{2}(5 - 2K) &= \frac{2}{\sqrt{2}} \\
5 - 2K &= \frac{2}{\sqrt{2}} \cdot \frac{1}{\sqrt{2}} \\
5 - 2K &= \frac{2}{2} \\
5 - 2K &= 1 \\
-2K &= -4 \\
K &= 2.
\end{align*}
Therefore, the value of K that satisfies the equation is 2.
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