Is the equation (2−3⋅22)(2√)−2=2%0D%0A(%0D%0A2%0D%0A−%0D%0A3%0D%0A⋅%0D%0A2%0D%0A2%0D%0A)%0D%0A(%0D%0A2%0D%0A)%0D%0A−%0D%0A2%0D%0A=%0D%0A2%0D%0A true or false? Select the response that correctly answers the question and provides the appropriate justification.

Question

Is the equation (2−3⋅22)(2√)−2=2%0D%0A(%0D%0A2%0D%0A−%0D%0A3%0D%0A⋅%0D%0A2%0D%0A2%0D%0A)%0D%0A(%0D%0A2%0D%0A)%0D%0A−%0D%0A2%0D%0A=%0D%0A2%0D%0A true or false? Select the response that correctly answers the question and provides the appropriate justification.

Answer 1

The equation is false.

To simplify the expression on the left side of the equation:

First, calculate within parentheses: (2−3⋅22) = (2−6).

Then, calculate the value inside the square root on the left side: 2√(2−6) = 2√(-4).

Since the square root of a negative number is not a real number, the left side of the equation does not have a defined value. Therefore, it cannot be equal to 2%0D%0A(%0D%0A2%0D%0A−%0D%0A3%0D%0A⋅%0D%0A2%0D%0A2%0D%0A)%0D%0A(%0D%0A2%0D%0A)%0D%0A−%0D%0A2%0D%0A=%0D%0A2%0D%0A.