Is 0.2 a root of \(x^2-0.4=0\)? Justify.
No.
To check if 0.2 is a root, we must put \(x = 0.2\) in the equation \(x^2 - 0.4 = 0\).
Step 1: Write the equation with \(x = 0.2\):
\((0.2)^2 - 0.4\)
Step 2: Find \((0.2)^2\):
\(0.2 \times 0.2 = 0.04\)
Step 3: Subtract 0.4 from 0.04:
\(0.04 - 0.4 = -0.36\)
Step 4: The result is \(-0.36\). For a number to be a root, the result must be exactly 0.
Since \(-0.36 \neq 0\), 0.2 is not a root of the equation.