To solve for \( \sqrt{823} - \sqrt{23} \), we start by approximating the square roots:
- \( \sqrt{823} \approx 28.7 \) (since \( 28^2 = 784 \) and \( 29^2 = 841 \)).
- \( \sqrt{23} \approx 4.8 \) (since \( 4^2 = 16 \) and \( 5^2 = 25 \)).
Now we perform the subtraction:
\[ \sqrt{823} - \sqrt{23} \approx 28.7 - 4.8 = 23.9 \]
Next, we compare this to the options provided to find the expression that matches best.
- \( \sqrt{823} \) is equivalent to approximately \( 28.7 \), therefore let's convert \( 23.9 \) and check which options seem plausible.
However, since the provided answer choices appear to be left as square root expressions:
Let’s square the original expression \( x = \sqrt{823} - \sqrt{23} \) and see if we can express it using square roots.
Setting \( x = \sqrt{823} - \sqrt{23} \), we can square both sides to get:
\[ x^2 = (\sqrt{823} - \sqrt{23})^2 \] \[ x^2 = 823 - 2\sqrt{823 \cdot 23} + 23 \] \[ x^2 = 846 - 2\sqrt{8469} \]
However, the above expression does not simplify easily nor yield a result corresponding to our answer choices.
The options seem to be square roots of other numbers:
- \( \sqrt{823} \)
- Roughly \( \sqrt{746} \)
- Roughly \( \sqrt{846} \)
- Roughly \( \sqrt{723} \)
Since none of the choices can be confirmed through simple estimations, further verification would be required with an exact numeric or calculator-based approach if one were available.
With these approximations alone, if we seek the square root expression that approximates \( 23.9 \):
The closest valid choice will be \( \sqrt{746} \) as all others were further from this approximate value per their numerical roots.
Thus, the correct option to select would be:
746−−√ (or \( \sqrt{746} \))