Let's solve the given equation:
[tex]\[
\sqrt{2 + 11} = 0
\][/tex]
First, simplify the expression under the square root:
[tex]\[
2 + 11 = 13
\][/tex]
So the equation becomes:
[tex]\[
\sqrt{13} = 0
\][/tex]
Recall that the square root of a non-negative number is the unique non-negative number that, when squared, gives the original number. In particular, the square root of a positive number is always positive. Therefore:
[tex]\[
\sqrt{13}
\][/tex]
is a positive number. Its approximate numerical value is 3.60555127546399.
Since a positive number cannot equal zero, the equation:
[tex]\[
\sqrt{13} = 0
\][/tex]
is not true. Thus, the original equation:
[tex]\[
\sqrt{2 + 11} = 0
\][/tex]
has no solutions.
In conclusion, the value of the left side is approximately 3.60555127546399, the value of the right side is 0, and they are not equal. Hence, the statement is false.
