# Solve for y square root of 7y-11 = square root of 9y-15 7y-11=9y-15
To remove the radical on the left side of the equation, square both sides of the equation.
7y-112=9y-152
Simplify each side of the equation.
Multiply the exponents in ((7y-11)12)2.
Apply the power rule and multiply exponents, (am)n=amn.
(7y-11)12⋅2=9y-152
Cancel the common factor of 2.
Cancel the common factor.
(7y-11)12⋅2=9y-152
Rewrite the expression.
(7y-11)1=9y-152
(7y-11)1=9y-152
(7y-11)1=9y-152
Simplify.
7y-11=9y-152
Factor 3 out of 9y-15.
Factor 3 out of 9y.
7y-11=3(3y)-152
Factor 3 out of -15.
7y-11=3(3y)+3(-5)2
Factor 3 out of 3(3y)+3(-5).
7y-11=3(3y-5)2
7y-11=3(3y-5)2
Rewrite 3(3y-5)2 as 3(3y-5).
Use axn=axn to rewrite 3(3y-5) as (3(3y-5))12.
7y-11=((3(3y-5))12)2
Apply the power rule and multiply exponents, (am)n=amn.
7y-11=(3(3y-5))12⋅2
Combine 12 and 2.
7y-11=(3(3y-5))22
Cancel the common factor of 2.
Cancel the common factor.
7y-11=(3(3y-5))22
Divide 1 by 1.
7y-11=(3(3y-5))1
7y-11=(3(3y-5))1
Simplify.
7y-11=3(3y-5)
7y-11=3(3y-5)
Apply the distributive property.
7y-11=3(3y)+3⋅-5
Multiply 3 by 3.
7y-11=9y+3⋅-5
Multiply 3 by -5.
7y-11=9y-15
7y-11=9y-15
Solve for y.
Move all terms containing y to the left side of the equation.
Subtract 9y from both sides of the equation.
7y-11-9y=-15
Subtract 9y from 7y.
-2y-11=-15
-2y-11=-15
Move all terms not containing y to the right side of the equation.
Add 11 to both sides of the equation.
-2y=-15+11
Add -15 and 11.
-2y=-4
-2y=-4
Divide each term by -2 and simplify.
Divide each term in -2y=-4 by -2.
-2y-2=-4-2
Cancel the common factor of -2.
Cancel the common factor.
-2y-2=-4-2
Divide y by 1.
y=-4-2
y=-4-2
Divide -4 by -2.
y=2
y=2
y=2
Solve for y square root of 7y-11 = square root of 9y-15

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