Think about the number of terms that each square root expression includes.
See solution.
Practice makes perfect
We are asked to compare the steps we take when we square sqrt(x+2) versus when we square sqrt(x)+2. To do so, let's first identify the number of terms that each of the square root expression includes.
sqrt(x+2) ⇒ & 1 term
sqrt(x)+ 2 ⇒ & 2 terms
As we can see, they have different numbers of terms. Therefore, we will examine what happens when we square monomial square root expressions and binomial square root expressions one at a time.
Squaring sqrt(x+2)
Let's begin by recalling that square roots and squaring a number are operations that undo each other.
sqrt(a) * sqrt(a) = a or (sqrt(a))^2=a
Since sqrt(x+2) is a monomial, when we square it, it eliminates the radical sign.
sqrt(x+2) * sqrt(x+2) =x+2
or
( sqrt(x+2))^() 2= x+2
The radicand of the square root is the answer when we square a monomial square root expression.
Squaring sqrt(x)+2
Since sqrt(x)+ 2 is a binomial expression, let's remember the rules for squaring binomials.
( a+ b)^() 2 = & a^2 +2 a b+ b^2
( a- b)^() 2 = & a^2 -2 a b+ b^2
Our expression uses addition, so we will apply the first formula. Let's substitute a= sqrt(x) and b= 2.
( sqrt(x)+ 2)^() 2 = & ( sqrt(x))^2 +2( sqrt(x))( 2)+( 2)^2
Great! Next, we will simplify the terms.
