# Simplify (2 square root of 5+ square root of 3)/(3 square root of 5+ square root of 3)

25+335+3
Multiply 25+335+3 by 35-335-3.
25+335+3⋅35-335-3
Combine fractions.
Multiply 25+335+3 and 35-335-3.
(25+3)(35-3)(35+3)(35-3)
Expand the denominator using the FOIL method.
(25+3)(35-3)952-315+315-32
Simplify.
(25+3)(35-3)42
(25+3)(35-3)42
Expand (25+3)(35-3) using the FOIL Method.
Apply the distributive property.
25(35-3)+3(35-3)42
Apply the distributive property.
25(35)+25(-3)+3(35-3)42
Apply the distributive property.
25(35)+25(-3)+3(35)+3(-3)42
25(35)+25(-3)+3(35)+3(-3)42
Simplify and combine like terms.
Simplify each term.
Multiply 25(35).
Multiply 3 by 2.
655+25(-3)+3(35)+3(-3)42
Raise 5 to the power of 1.
6(515)+25(-3)+3(35)+3(-3)42
Raise 5 to the power of 1.
6(5151)+25(-3)+3(35)+3(-3)42
Use the power rule aman=am+n to combine exponents.
651+1+25(-3)+3(35)+3(-3)42
652+25(-3)+3(35)+3(-3)42
652+25(-3)+3(35)+3(-3)42
Rewrite 52 as 5.
Use axn=axn to rewrite 5 as 512.
6(512)2+25(-3)+3(35)+3(-3)42
Apply the power rule and multiply exponents, (am)n=amn.
6⋅512⋅2+25(-3)+3(35)+3(-3)42
Combine 12 and 2.
6⋅522+25(-3)+3(35)+3(-3)42
Cancel the common factor of 2.
Cancel the common factor.
6⋅522+25(-3)+3(35)+3(-3)42
Divide 1 by 1.
6⋅51+25(-3)+3(35)+3(-3)42
6⋅51+25(-3)+3(35)+3(-3)42
Evaluate the exponent.
6⋅5+25(-3)+3(35)+3(-3)42
6⋅5+25(-3)+3(35)+3(-3)42
Multiply 6 by 5.
30+25(-3)+3(35)+3(-3)42
Multiply 25(-3).
Multiply -1 by 2.
30-253+3(35)+3(-3)42
Combine using the product rule for radicals.
30-23⋅5+3(35)+3(-3)42
Multiply 3 by 5.
30-215+3(35)+3(-3)42
30-215+3(35)+3(-3)42
Multiply 3(35).
Combine using the product rule for radicals.
30-215+33⋅5+3(-3)42
Multiply 3 by 5.
30-215+315+3(-3)42
30-215+315+3(-3)42
Multiply 3(-3).
Raise 3 to the power of 1.
30-215+315-(313)42
Raise 3 to the power of 1.
30-215+315-(3131)42
Use the power rule aman=am+n to combine exponents.
30-215+315-31+142
30-215+315-3242
30-215+315-3242
Rewrite 32 as 3.
Use axn=axn to rewrite 3 as 312.
30-215+315-(312)242
Apply the power rule and multiply exponents, (am)n=amn.
30-215+315-312⋅242
Combine 12 and 2.
30-215+315-32242
Cancel the common factor of 2.
Cancel the common factor.
30-215+315-32242
Divide 1 by 1.
30-215+315-3142
30-215+315-3142
Evaluate the exponent.
30-215+315-1⋅342
30-215+315-1⋅342
Multiply -1 by 3.
30-215+315-342
30-215+315-342
Subtract 3 from 30.
27-215+31542
27+1542
27+1542
The result can be shown in multiple forms.
Exact Form:
27+1542
Decimal Form:
0.73507103…
Simplify (2 square root of 5+ square root of 3)/(3 square root of 5+ square root of 3)

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