Consider the equation 43⋅(64−−√3)2=46

Question

. Is this equation true or false? Enter 1 for true or 2 for false.(1 point)

Answer 1

To determine whether the equation \( 43 \cdot (64^{1/2} \cdot 3)^2 = 46 \) is true or false, we need to simplify the left side and compare it to 46.

First, calculate \( 64^{1/2} \): \[ 64^{1/2} = 8 \]

Now, substitute this into the equation: \[ 43 \cdot (8 \cdot 3)^2 \]

Next, calculate \( (8 \cdot 3) \): \[ 8 \cdot 3 = 24 \]

Now, calculate \( 24^2 \): \[ 24^2 = 576 \]

Now substitute that back into the equation: \[ 43 \cdot 576 \]

Now perform the multiplication: \[ 43 \cdot 576 = 24768 \]

Now we check if: \[ 24768 = 46 \] This is clearly false.

Thus, the equation is false. The answer is \( 2 \).