√(5 + x)2 =

Question

√(5 + x)2 =

anonymous · Answer

5+x^2

compassionate · Answer

Hello! 

This one isn't too hard. Basically, we want the square root of something, right? Now what is the opposite of square rooting something? That's it! Putting it to the second power. 

For example: $$2^2 = 4, \sqrt{4} = 2$$ This is a simple relationship. A sqaure root is basically saying, "If this number is multiplied by itself, what number will I get? Will it be this number?" 

For example, the square root of 9 is 3. However, there is no square root for 7, becuase no two whole numbers, when multiplied, will equal seven. But if you notice, putting a number to the power of two will undo that operation.

One more example$$3^2 = 9, \sqrt{9} =3$$

Therefore, $$\sqrt{(5+ x)^2} = ?$$

parthkohli · Answer

Just saying... but if $\sqrt{(-3)^2} = 9$, then why is $\sqrt{9} \ne -3$?

compassionate · Answer

@BrianR07 , try to work with me, please (:

parthkohli · Answer

We can now extend our theory.$$\sqrt{(-3)^2} =3$$$$\sqrt{(-4)^2}=4$$So basically, we see that when you have $x$ a negative number, then$$\sqrt{(x)^2} = -x \qquad \rm for~ x ~ negative$$In other words, whatever sign of $x$ you have, you bring in the positive sign.  This is also known as the absolute value of $x$ or $|x|$.  Finally,$$\sqrt{x^2}=|x|$$

compassionate · Answer

Therefore, in essence, any squared term in a square root will just be the absolute term itself. 

$$\sqrt{(x - y)^2} = |(x - y)|$$