$\frac{260}{37}+\sqrt{198}+\sqrt[3]{?}=5^2$
What approximate value should come in place of the question mark (?) in the following questions?

To find the approximate value that should replace the question mark (?), let's analyze the given equation:

$\frac{260}{37}+\sqrt{198}+\sqrt[3]{?}=5^2$

We will approximate each term in the equation step-by-step:

1. Approximating the first term:
Let's look at the fraction $\frac{260}{37}$.
Since $37\times 7=259$, the value of $\frac{260}{37}$ is extremely close to 7.
Therefore, $\frac{260}{37}\approx 7$.

2. Approximating the second term:
Let's find the square root of 198, i.e., $\sqrt{198}$.
We know that the nearest perfect square to 198 is 196, and $\sqrt{196}=14$.
Thus, $\sqrt{198}\approx 14$.

3. Evaluating the right side of the equation:
$5^2=25$

4. Substituting these approximations back into the equation:
$7+14+\sqrt[3]{?}\approx 25$
$21+\sqrt[3]{?}\approx 25$
$\sqrt[3]{?}\approx 25-21$
$\sqrt[3]{?}\approx 4$

5. Solving for ?:
To find the value of ?, we cube both sides of the equation:
$?\approx 4^3$
$?\approx 4\times 4\times 4$
$?\approx 64$

Therefore, the approximate value that should come in place of the question mark is 64.