Square Root Calculation

First, we need to find the square root of 2401. We are looking for a number which, when multiplied by itself, equals 2401.

Let's test some numbers:

• We know that $40^2 = 1600$ and $50^2 = 2500$. So the square root of 2401 must be between 40 and 50.
• Since 2401 ends in 1, the square root must end in either 1 or 9.
• Let's try 49: $49 \times 49 = 2401$.

So, the square root of 2401 is 49.

We can write this mathematically as:

$\sqrt{2401} = 49$

Multiplication Operations

Next, we perform the multiplication operations in the equation:

• Calculate $6 \times 4$: $6 \times 4 = 24$.
• Calculate $32 \times 9$: $32 \times 9 = 288$.

Equation Simplification

Now, let's substitute these values back into the original equation:

$\sqrt{2401} + 6 \times 4 = ?^2 – 32 \times 9$

Substituting the calculated values:

$49 + 24 = ?^2 – 288$

Simplify the left side of the equation:

$73 = ?^2 – 288$

Finding the Unknown Value

To find the value of $?^2$, we need to isolate it. We can do this by adding 288 to both sides of the equation:

$73 + 288 = ?^2$

Calculate the sum:

$361 = ?^2$

Finally, to find the value of '?', we take the square root of 361:

$? = \sqrt{361}$

We know that $19 \times 19 = 361$.

Therefore, $? = 19$.

Conclusion

The value that replaces the question mark ‘?’ in the equation is 19.