Question

What is the value of this expression?

(12)2+23+8−−−−−√

Enter your answer in the box as a mixed number in simplest form.

Answer 1

To evaluate the expression \((12)2 + 23 + \sqrt{8}\), we first break it down into its components.

1. Calculate \((12)2\):
\[
(12)2 = 12 \times 2 = 24
\]

2. Calculate \(23\):
\[
23 = 23
\]

3. Calculate \(\sqrt{8}\):
Since \(8 = 4 \times 2\), we can simplify \(\sqrt{8}\):
\[
\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}
\]

Now, substituting these values back into the expression, we have:
\[
24 + 23 + 2\sqrt{2}
\]
Combining the constants:
\[
24 + 23 = 47
\]
So, the expression simplifies to:
\[
47 + 2\sqrt{2}
\]

To express \(2\sqrt{2}\) as a mixed number, we need to approximate \(\sqrt{2}\).
Using the approximation \(\sqrt{2} \approx 1.414\):
\[
2\sqrt{2} \approx 2 \times 1.414 = 2.828
\]

Now, we can convert \(47 + 2.828\):
\[
47 + 2.828 \approx 49.828
\]

To express \(49.828\) as a mixed number, we take the integer part and the fractional part:
- The integer part is \(49\).
- The fractional part is \(0.828\). Converting \(0.828\) to a fraction, we can approximate it as \(\frac{828}{1000}\), which simplifies to \(\frac{207}{250}\).

Thus, the expression \(49 + 0.828\) can be expressed as the mixed number:
\[
49 \frac{207}{250}
\]

Finally, the answer in simplest mixed number form is:
\[
\boxed{49 \frac{207}{250}}
\]