# Simplify ( square root of 82)/(9- square root of 82) 829-82
Multiply 829-82 by 9+829+82.
829-82⋅9+829+82
Simplify terms.
Multiply 829-82 and 9+829+82.
82(9+82)(9-82)(9+82)
Expand the denominator using the FOIL method.
82(9+82)81+982-982-822
Simplify.
82(9+82)-1
Simplify the expression.
Move the negative one from the denominator of 82(9+82)-1.
-1⋅(82(9+82))
Rewrite -1⋅(82(9+82)) as -(82(9+82)).
-(82(9+82))
-(82(9+82))
Apply the distributive property.
-(82⋅9+8282)
Move 9 to the left of 82.
-(9⋅82+8282)
Combine using the product rule for radicals.
-(9⋅82+82⋅82)
-(9⋅82+82⋅82)
Simplify each term.
Multiply 82 by 82.
-(982+6724)
Rewrite 6724 as 822.
-(982+822)
Pull terms out from under the radical, assuming positive real numbers.
-(982+82)
-(982+82)
Simplify by multiplying through.
Apply the distributive property.
-(982)-1⋅82
Multiply.
Multiply 9 by -1.
-982-1⋅82
Multiply -1 by 82.
-982-82
-982-82
-982-82
The result can be shown in multiple forms.
Exact Form:
-982-82
Decimal Form:
-163.49846624…
Simplify ( square root of 82)/(9- square root of 82)

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