# Solve for y square root of 5y-3 = square root of y+8

5y-3=y+8
To remove the radical on the left side of the equation, square both sides of the equation.
5y-32=y+82
Simplify each side of the equation.
Multiply the exponents in ((5y-3)12)2.
Apply the power rule and multiply exponents, (am)n=amn.
(5y-3)12⋅2=y+82
Cancel the common factor of 2.
Cancel the common factor.
(5y-3)12⋅2=y+82
Rewrite the expression.
(5y-3)1=y+82
(5y-3)1=y+82
(5y-3)1=y+82
Simplify.
5y-3=y+82
Rewrite y+82 as y+8.
Use axn=axn to rewrite y+8 as (y+8)12.
5y-3=((y+8)12)2
Apply the power rule and multiply exponents, (am)n=amn.
5y-3=(y+8)12⋅2
Combine 12 and 2.
5y-3=(y+8)22
Cancel the common factor of 2.
Cancel the common factor.
5y-3=(y+8)22
Divide 1 by 1.
5y-3=(y+8)1
5y-3=(y+8)1
Simplify.
5y-3=y+8
5y-3=y+8
5y-3=y+8
Solve for y.
Move all terms containing y to the left side of the equation.
Subtract y from both sides of the equation.
5y-3-y=8
Subtract y from 5y.
4y-3=8
4y-3=8
Move all terms not containing y to the right side of the equation.
Add 3 to both sides of the equation.
4y=8+3
4y=11
4y=11
Divide each term by 4 and simplify.
Divide each term in 4y=11 by 4.
4y4=114
Cancel the common factor of 4.
Cancel the common factor.
4y4=114
Divide y by 1.
y=114
y=114
y=114
y=114
The result can be shown in multiple forms.
Exact Form:
y=114
Decimal Form:
y=2.75
Mixed Number Form:
y=234
Solve for y square root of 5y-3 = square root of y+8

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