Discussion
Simplify the following expression:
\(\left[347^{0.5}\times 1388^{0.5}\right]\div\left[16^{0.16}\times 2^{0.36}\right]\)
Answer: A
The value is 347.
The numerator is \(347^{0.5}\times 1388^{0.5}=\sqrt{347\times1388}=\sqrt{481636}=694\). The denominator is \(16^{0.16}\times 2^{0.36}=2^{0.64}\times2^{0.36}=2^{1}=2\), since 16 is 2 to the power 4.
\[ \frac{694}{2}=347 \]
694, 447 and 894 do not follow from these steps.
A quick check of the numerator: 347 × 1388 equals 481636, and 694 × 694 is also 481636, so the square root is exactly 694. The power 0.16 of 16 is 2 raised to 4 × 0.16 = 0.64, and 0.64 + 0.36 = 1, which makes the denominator 2.
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