MarkFL said:That only works if $A$ is non-negative. More precisely, there is the definition:
\(\displaystyle |A|\equiv\sqrt{A^2}\)
Let's now assume that $0\le A$. Then we can think of this along these lines:
\(\displaystyle \sqrt{A^2}=\left(A^2\right)^{\frac{1}{2}}=A^{2\cdot\frac{1}{2}}=A^1=A\)
It doesn't. If A= -2 then A^2= 4 and sqrt(4)= 2 not -2.RTCNTC said:Let A be an a algebraic term.
Why does the sqrt{(A)^2} = A?
In other words, why does the radicand simply come out of the square root?
greg1313 said:Yes, but only because $x^2+1=|x^2+1|$, as $x^2+1$ is always positive.
greg1313 said:Are you familiar with absolute value?
"Sqrt" stands for square root and "(something)^2" represents a number or expression raised to the power of 2. Therefore, "Sqrt{(something)^2}" means the square root of a number or expression squared.
To solve for the value of "Sqrt{(something)^2}", you first need to find the square root of the number or expression inside the parentheses. Then, square the result to get the final answer. For example, if "something" is 4, then "Sqrt{(something)^2}" would be equal to 4.
The expression "Sqrt{(something)^2}" and absolute value are closely related. The square root of a number squared will always result in the absolute value of that number. In other words, "Sqrt{(something)^2}" is another way of expressing the absolute value of "something".
No, the square root of any number squared will always be positive. This is because squaring a negative number will result in a positive number, and taking the square root of a positive number will also result in a positive number.
The square root of a number squared is commonly used in various mathematical and scientific calculations, such as finding the distance between two points on a coordinate plane or calculating the magnitude of a vector. It is also used to solve equations involving quadratic functions and to find the length of the hypotenuse in a right triangle.