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.