Simplify \(\frac{\sqrt{128}}{\sqrt{32} - 2\sqrt{2}}\)
Question 1 Report
Simplify \(\frac{\sqrt{128}}{\sqrt{32} - 2\sqrt{2}}\)
Answer Details
We can start by simplifying the numerator and the denominator separately.
The square root of 128 can be written as the square root of 64 times 2, which simplifies to 8 times the square root of 2.
The denominator can be simplified using the difference of squares formula:
\begin{align*}
\sqrt{32} - 2\sqrt{2} &= \sqrt{16 \times 2} - 2\sqrt{2} \\
&= 4\sqrt{2} - 2\sqrt{2} \\
&= 2\sqrt{2}
\end{align*}
Now we can substitute these simplifications back into the original expression:
\begin{align*}
\frac{\sqrt{128}}{\sqrt{32} - 2\sqrt{2}} &= \frac{8\sqrt{2}}{2\sqrt{2}} \\
&= 4
\end{align*}
Therefore, the simplified expression is 4.
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