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

Math
4+b2=(83)2
Simplify (83)2.
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Simplify the expression.
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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.
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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.
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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
Move all terms not containing b to the right side of the equation.
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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
The complete solution is the result of both the positive and negative portions of the solution.
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Simplify the right side of the equation.
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Rewrite 188 as 22⋅47.
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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.
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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

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