# Solve for y square root of y^2-16 = square root of 16+3

y2-16=16+3
To remove the radical on the left side of the equation, square both sides of the equation.
y2-162=16+32
Simplify each side of the equation.
Multiply the exponents in ((y2-16)12)2.
Apply the power rule and multiply exponents, (am)n=amn.
(y2-16)12⋅2=16+32
Cancel the common factor of 2.
Cancel the common factor.
(y2-16)12⋅2=16+32
Rewrite the expression.
(y2-16)1=16+32
(y2-16)1=16+32
(y2-16)1=16+32
Simplify.
y2-16=16+32
y2-16=192
Rewrite 192 as 19.
Use axn=axn to rewrite 19 as 1912.
y2-16=(1912)2
Apply the power rule and multiply exponents, (am)n=amn.
y2-16=1912⋅2
Combine 12 and 2.
y2-16=1922
Cancel the common factor of 2.
Cancel the common factor.
y2-16=1922
Divide 1 by 1.
y2-16=191
y2-16=191
Evaluate the exponent.
y2-16=19
y2-16=19
y2-16=19
Solve for y.
Move all terms not containing y to the right side of the equation.
Add 16 to both sides of the equation.
y2=19+16
y2=35
y2=35
Take the square root of both sides of the equation to eliminate the exponent on the left side.
y=±35
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
y=35
Next, use the negative value of the ± to find the second solution.
y=-35
The complete solution is the result of both the positive and negative portions of the solution.
y=35,-35
y=35,-35
y=35,-35
The result can be shown in multiple forms.
Exact Form:
y=35,-35
Decimal Form:
y=5.91607978…,-5.91607978…
Solve for y square root of y^2-16 = square root of 16+3

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