Equation Calculation: (18 × 6) - (52 × 4) = √?

This problem requires us to simplify a mathematical equation involving multiplication, subtraction, and a square root to find the value represented by the question mark (?). Let's break down the calculation step-by-step.

Calculate Left Side Value

First, we evaluate the expression on the left side of the equation:

Left Side = $$(18 \times 6) - (52 \times 4)$$

Let's perform the multiplications:

• $$18 \times 6 = 108$$
• $$52 \times 4 = 208$$

Now, substitute these results back into the expression:

Left Side = $$108 - 208$$

Performing the subtraction:

Left Side = $$-100$$

The Resulting Equation

Now we have the simplified equation:

$$-100 = \sqrt{?}$$

Analyze Provided Options

The question asks for the value that should replace the question mark (?). The provided options are:

We need to determine which of these values for ? satisfies the equation -100 = √?.

Check Answer Option 64

The indicated correct answer is option 4, which means ? = 64. Let's substitute this value into the equation:

Equation: $$-100 = \sqrt{?}$$

Substitute ? = 64:

$$-100 = \sqrt{64}$$

Calculate the square root of 64:

$$\sqrt{64} = 8$$

So, the equation becomes:

$$-100 = 8$$

This statement is mathematically incorrect, as -100 does not equal 8.

Summarize Calculation Steps

We performed the calculations on the left side of the equation, resulting in -100. The equation is thus -100 = √?. Testing the provided answer option ? = 64 leads to -100 = 8, which is false. If we were to solve -100 = √? for ?, squaring both sides would yield ? = (-100)^2 = 10000. If we assume the equation meant √? = 64, then ? = 64^2 = 4096. Neither of these calculated values match the options provided.

The solution demonstrates the calculation steps as per the question asked.