Is the equation 7−4⋅7349√=7

Question

true or false? Select the response that correctly answers the question and provides the appropriate justification.

Answer 1

To evaluate the equation $7-4\cdot \sqrt{7349}=7$, we can start by isolating the term on the left side and seeing if it equals $7$.

First, we'll simplify the left side:

1. Start with the equation: $$7-4\cdot \sqrt{7349}=7$$

2. Subtract $7$ from both sides: $$-4\cdot \sqrt{7349}=0$$

3. To isolate $\sqrt{7349}$, we multiply both sides by $-1$: $$4\cdot \sqrt{7349}=0$$

4. Now, divide both sides by $4$: $$\sqrt{7349}=0$$

Since the square root of a positive number cannot be zero, we can conclude that $\sqrt{7349}$ is not equal to zero. Thus, the left side cannot equal the right side $7$.

Therefore, the equation $7-4\cdot \sqrt{7349}=7$ is false.

Justification: The equation implies that $\sqrt{7349}$ would have to be zero, which is impossible since $7349$ is a positive number.