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

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

Add 16 and 3.

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

Move all terms not containing y to the right side of the equation.

Add 16 to both sides of the equation.

y2=19+16

Add 19 and 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