4+b2=(83)2

Simplify the expression.

Apply the product rule to 83.

4+b2=8232

Raise 8 to the power of 2.

4+b2=6432

4+b2=6432

Rewrite 32 as 3.

Use axn=axn to rewrite 3 as 312.

4+b2=64(312)2

Apply the power rule and multiply exponents, (am)n=amn.

4+b2=64⋅312⋅2

Combine 12 and 2.

4+b2=64⋅322

Cancel the common factor of 2.

Cancel the common factor.

4+b2=64⋅322

Divide 1 by 1.

4+b2=64⋅31

4+b2=64⋅31

Evaluate the exponent.

4+b2=64⋅3

4+b2=64⋅3

Multiply 64 by 3.

4+b2=192

4+b2=192

Subtract 4 from both sides of the equation.

b2=192-4

Subtract 4 from 192.

b2=188

b2=188

Take the square root of both sides of the equation to eliminate the exponent on the left side.

b=±188

Simplify the right side of the equation.

Rewrite 188 as 22⋅47.

Factor 4 out of 188.

b=±4(47)

Rewrite 4 as 22.

b=±22⋅47

b=±22⋅47

Pull terms out from under the radical.

b=±247

b=±247

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.

b=247

Next, use the negative value of the ± to find the second solution.

b=-247

The complete solution is the result of both the positive and negative portions of the solution.

b=247,-247

b=247,-247

b=247,-247

The result can be shown in multiple forms.

Exact Form:

b=247,-247

Decimal Form:

b=13.71130920…,-13.71130920…

Solve using the Square Root Property 4+b^2=(8 square root of 3)^2