# Simplify ( square root of 7- square root of 13)( square root of 7+ square root of 13)

(7-13)(7+13)
Expand (7-13)(7+13) using the FOIL Method.
Apply the distributive property.
7(7+13)-13(7+13)
Apply the distributive property.
77+713-13(7+13)
Apply the distributive property.
77+713-137-1313
77+713-137-1313
Simplify and combine like terms.
Simplify each term.
Combine using the product rule for radicals.
7⋅7+713-137-1313
Multiply 7 by 7.
49+713-137-1313
Rewrite 49 as 72.
72+713-137-1313
Pull terms out from under the radical, assuming positive real numbers.
7+713-137-1313
Combine using the product rule for radicals.
7+7⋅13-137-1313
Multiply 7 by 13.
7+91-137-1313
Multiply -137.
Combine using the product rule for radicals.
7+91-7⋅13-1313
Multiply 7 by 13.
7+91-91-1313
7+91-91-1313
Multiply -1313.
Raise 13 to the power of 1.
7+91-91-(13113)
Raise 13 to the power of 1.
7+91-91-(131131)
Use the power rule aman=am+n to combine exponents.
7+91-91-131+1
7+91-91-132
7+91-91-132
Rewrite 132 as 13.
Use axn=axn to rewrite 13 as 1312.
7+91-91-(1312)2
Apply the power rule and multiply exponents, (am)n=amn.
7+91-91-1312⋅2
Combine 12 and 2.
7+91-91-1322
Cancel the common factor of 2.
Cancel the common factor.
7+91-91-1322
Divide 1 by 1.
7+91-91-131
7+91-91-131
Evaluate the exponent.
7+91-91-1⋅13
7+91-91-1⋅13
Multiply -1 by 13.
7+91-91-13
7+91-91-13
Subtract 13 from 7.
-6+91-91
Subtract 91 from 91.
-6+0