What approximate value should come in place of question mark (?) in the following equation.

${\left(24.01\right)}^2+\sqrt[3]{63.98}-{\left(21.99\right)}^2=\frac{?}{10.98}$

The correct answer is 1056.

To solve for the approximate value of the question mark (?), we can round each term in the given equation to its nearest whole number or convenient value.

The given equation is:

${\left(24.01\right)}^2+\sqrt[3]{63.98}-{\left(21.99\right)}^2=\frac{?}{10.98}$

Now, let us approximate each term step-by-step:

1. 24.01 can be rounded to 24.
2. 63.98 can be rounded to 64, and the cube root of 64 is 4 since 4³ = 64.
3. 21.99 can be rounded to 22.
4. 10.98 in the denominator can be rounded to 11.

Substituting these approximate values into the equation:

${\left(24\right)}^2+\sqrt[3]{64}-{\left(22\right)}^2=\frac{?}{11}$

Calculate the squares and the cube root:
24² = 576
$\sqrt[3]{64}$ = 4
22² = 484

Now substitute these evaluated values back into the left side of the equation:

$576+4-484=\frac{?}{11}$

Simplify the left hand side:
576 + 4 = 580
580 - 484 = 96

So, the simplified equation is:

$96=\frac{?}{11}$

Now, multiply both sides by 11 to solve for ?:

$?=96\times 11$

? = 1056

Therefore, the approximate value that should come in place of the question mark (?) is 1056.