Hello!
The answer is:
a) Her reasoning is incorrect, she applied a wrong operation, the way to simplify the expression was using the square root property. If we want to extract a number of a square root, we must square that number first in order not to modify the expression.
b) We have that:
[tex]\sqrt{200}=14.14[/tex]
and rounding to the nearest tenth, we have that:
[tex]\sqrt{200}=14.1[/tex]
Why?
To solve the problem, we need to remember the following property of square roots:
[tex]\sqrt{ab}=\sqrt{a}*\sqrt{b}[/tex]
We are given the expression:
[tex]\sqrt{200}[/tex]
We can rewrite it by the following way:
[tex]\sqrt{100*2}[/tex]
Now, applying the square root property we have:
[tex]\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}=14.14[/tex]
Therefore,
a) Her reasoning was wrong, she applied a wrong operation, the way to simplify the expression was using the square root property. If we want to extract a number of a square root, we must square that number first in order not to modify the expression.
b) We have that:
[tex]\sqrt{200}=14.14[/tex]
and rounding to the nearest tenth, we have that:
[tex]\sqrt{200}=14.1[/tex]
Have a nice day!
