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

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

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

Add 8 and 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