Simplify ( square root of 7)/( square root of 11)+( square root of 11)/( square root of 7)

Math
711+117
Simplify each term.
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Multiply 711 by 1111.
711⋅1111+117
Combine and simplify the denominator.
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Multiply 711 and 1111.
7111111+117
Raise 11 to the power of 1.
71111111+117
Raise 11 to the power of 1.
711111111+117
Use the power rule aman=am+n to combine exponents.
711111+1+117
Add 1 and 1.
711112+117
Rewrite 112 as 11.
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Use axn=axn to rewrite 11 as 1112.
711(1112)2+117
Apply the power rule and multiply exponents, (am)n=amn.
7111112⋅2+117
Combine 12 and 2.
7111122+117
Cancel the common factor of 2.
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Cancel the common factor.
7111122+117
Divide 1 by 1.
711111+117
711111+117
Evaluate the exponent.
71111+117
71111+117
71111+117
Simplify the numerator.
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Combine using the product rule for radicals.
7⋅1111+117
Multiply 7 by 11.
7711+117
7711+117
Multiply 117 by 77.
7711+117⋅77
Combine and simplify the denominator.
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Multiply 117 and 77.
7711+11777
Raise 7 to the power of 1.
7711+117717
Raise 7 to the power of 1.
7711+1177171
Use the power rule aman=am+n to combine exponents.
7711+11771+1
Add 1 and 1.
7711+11772
Rewrite 72 as 7.
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Use axn=axn to rewrite 7 as 712.
7711+117(712)2
Apply the power rule and multiply exponents, (am)n=amn.
7711+117712⋅2
Combine 12 and 2.
7711+117722
Cancel the common factor of 2.
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Cancel the common factor.
7711+117722
Divide 1 by 1.
7711+11771
7711+11771
Evaluate the exponent.
7711+1177
7711+1177
7711+1177
Simplify the numerator.
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Combine using the product rule for radicals.
7711+11⋅77
Multiply 11 by 7.
7711+777
7711+777
7711+777
To write 7711 as a fraction with a common denominator, multiply by 77.
7711⋅77+777
To write 777 as a fraction with a common denominator, multiply by 1111.
7711⋅77+777⋅1111
Write each expression with a common denominator of 77, by multiplying each by an appropriate factor of 1.
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Multiply 7711 and 77.
77⋅711⋅7+777⋅1111
Multiply 11 by 7.
77⋅777+777⋅1111
Multiply 777 and 1111.
77⋅777+77⋅117⋅11
Multiply 7 by 11.
77⋅777+77⋅1177
77⋅777+77⋅1177
Combine the numerators over the common denominator.
77⋅7+77⋅1177
Simplify the numerator.
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Move 7 to the left of 77.
7⋅77+77⋅1177
Move 11 to the left of 77.
777+11⋅7777
Add 777 and 1177.
187777
187777
The result can be shown in multiple forms.
Exact Form:
187777
Decimal Form:
2.05129037…
Simplify ( square root of 7)/( square root of 11)+( square root of 11)/( square root of 7)

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