Basic Algebra

Hi

So you have to solve for x right? so you have to "get rid" of the exponent, you can do that by taking the square root of each side

x^2=4
root(X^2)=root(4)

that works because the square root is the same thing as raising something to the power of 1/2 so

(x^2)^1/2=x^(2/2)=x^1=x

hope that helps
 
rbcc said:
So you have to solve for x right? so you have to "get rid" of the exponent, you can do that by taking the square root of each side

x^2=4
root(X^2)=root(4)

that works because the square root is the same thing as raising something to the power of 1/2 so

(x^2)^1/2=x^(2/2)=x^1=x
Click to expand...

rbcc's approach misses the solution x = -2.

The square root of x^2 is not x. It is |x|.

Hence, when you take the square root of both sides of the equation x^2 = 4, you get:

|x| = 2

Removing the absolute-value symbols requires considering both numbers whose absolute value is 2:

x = ±2



The expressions √(x^2) and (x^2)^(1/2) each represent the "Principle Square Root" of x^2.

When x^2 = 4, the principal square root is 2, but every positive Real number has two roots, so -2 is the other.

You can read more about this here and here.



Something else to keep in mind:

When you're given the expression √n, it represents one number: the principal square root of the number n.

When you're given n and you take the square root of n (during the process of solving an equation), then the expression √n may give rise to two numbers: the principle square root and its opposite, and you need to consider both, or you could miss solution(s).

Cheers ~ Mark :cool:
 
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