# Solve for a square root of 5a-2 = square root of a+6

5a-2=a+6
To remove the radical on the left side of the equation, square both sides of the equation.
5a-22=a+62
Simplify each side of the equation.
Multiply the exponents in ((5a-2)12)2.
Apply the power rule and multiply exponents, (am)n=amn.
(5a-2)12⋅2=a+62
Cancel the common factor of 2.
Cancel the common factor.
(5a-2)12⋅2=a+62
Rewrite the expression.
(5a-2)1=a+62
(5a-2)1=a+62
(5a-2)1=a+62
Simplify.
5a-2=a+62
Rewrite a+62 as a+6.
Use axn=axn to rewrite a+6 as (a+6)12.
5a-2=((a+6)12)2
Apply the power rule and multiply exponents, (am)n=amn.
5a-2=(a+6)12⋅2
Combine 12 and 2.
5a-2=(a+6)22
Cancel the common factor of 2.
Cancel the common factor.
5a-2=(a+6)22
Divide 1 by 1.
5a-2=(a+6)1
5a-2=(a+6)1
Simplify.
5a-2=a+6
5a-2=a+6
5a-2=a+6
Solve for a.
Move all terms containing a to the left side of the equation.
Subtract a from both sides of the equation.
5a-2-a=6
Subtract a from 5a.
4a-2=6
4a-2=6
Move all terms not containing a to the right side of the equation.
Add 2 to both sides of the equation.
4a=6+2
4a=8
4a=8
Divide each term by 4 and simplify.
Divide each term in 4a=8 by 4.
4a4=84
Cancel the common factor of 4.
Cancel the common factor.
4a4=84
Divide a by 1.
a=84
a=84
Divide 8 by 4.
a=2
a=2
a=2
Solve for a square root of 5a-2 = square root of a+6