What is the square root property and what is it used for?

Asked on by monique06

llltkl | College Teacher | (Level 3) Valedictorian

Posted on

The square root property is one method that is used to find the solutions to a quadratic equation of the type `(ax+b)^2 = c or, x^2 = c`   This method involves taking the square roots of both sides of the equation.  There is a possibility of two roots for every squared term, one positive and one negative, as both of these when squared give the same result.  That is why a `+-` sign is inserted front of the side containing the constant, before taking the square root of that side.

Example: solve: `(x-2)^2 = 16`

the squared-variable term is isolated, so we will take the square root of each side

`=>sqrt((x-2)^2)=+- sqrt(16)`
now simplify the radicals,

`x-2 = +-4`

`+-4` are rational numbers, which means

x-2 = +4 and x-2 =-4

hence x= 6 and -2, both these solutions are possible.

Sources:

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