Chapter Test
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Rearrange the radical equation so that the radical expression is isolated. Then raise both sides of the equation to the second power.
7/3
We will find and check the solution of the given equation.
To solve an equation with a variable expression inside a radical, we will first rearrange the radical equation so that the radical expression is isolated. Then, we can raise both sides of the equation to a power equal to the index of the radical. In this case, we will raise both sides of the equation to the second power. Let's do it!
LHS * 3=RHS* 3
LHS^2=RHS^2
( sqrt(a) )^2 = a
Calculate power
LHS-2=RHS-2
.LHS /3.=.RHS /3.
The solution of our equation is m = 73. Now, let's check whether our solution is extraneous.
To check our solution, we will substitute 73 for m into the original equation. If we obtain a true statement, the solution is not extraneous. Otherwise, the solution is extraneous.
m= 7/3
3 * a/3= a
Add terms
Calculate root
a/a=1
We obtained a true statement, so m= 73 is a solution to the equation.