$?\times \sqrt{170}=26\frac{\sqrt[3]{127}}{6}\times 6\frac{\sqrt{330}}{23}$What approximate value should come in place of the question mark (?) in the following questions?

To find the approximate value that should come in place of the question mark (?), we can simplify each term in the given equation to its nearest convenient value.

The given equation is:
$?\times \sqrt{170}=26\frac{\sqrt[3]{127}}{6}\times 6\frac{\sqrt{330}}{23}$

Let's approximate each term step-by-step:

1. Approximating the left-hand side square root term:
Since 169 is a perfect square (${13}^2=169$):
$\sqrt{170}\approx \sqrt{169}=13$

2. Approximating the first mixed fraction term:
First, approximate the cube root in the numerator. Since 125 is a perfect cube ($5^3=125$):
$\sqrt[3]{127}\approx \sqrt[3]{125}=5$
Substituting this back gives:
$26\frac{\sqrt[3]{127}}{6}\approx 26\frac{5}{6}=26+0.833=26.833$

3. Approximating the second mixed fraction term:
First, approximate the square root in the numerator. Since 324 is a perfect square (${18}^2=324$):
$\sqrt{330}\approx \sqrt{324}=18$
Substituting this back gives:
$6\frac{\sqrt{330}}{23}\approx 6\frac{18}{23}\approx 6+0.783=6.783$

4. Calculating the product on the right-hand side:
Now, multiply the two approximated values:
$26.833\times 6.783\approx 182$

5. Solving for the question mark (?):
Let the question mark be represented by $x$:
$x\times 13\approx 182$
$x\approx \frac{182}{13}$
$x\approx 14$

Therefore, the approximate value that should come in place of the question mark is 14.