# Simplify 1/( square root of 3)*(( square root of 5)/2)+1/( square root of 3)*(1/2)

13⋅(52)+13⋅(12)
Multiply 13 by 33.
13⋅33⋅52+13⋅(12)
Combine and simplify the denominator.
Multiply 13 and 33.
333⋅52+13⋅(12)
Raise 3 to the power of 1.
3313⋅52+13⋅(12)
Raise 3 to the power of 1.
33131⋅52+13⋅(12)
Use the power rule aman=am+n to combine exponents.
331+1⋅52+13⋅(12)
332⋅52+13⋅(12)
Rewrite 32 as 3.
Use axn=axn to rewrite 3 as 312.
3(312)2⋅52+13⋅(12)
Apply the power rule and multiply exponents, (am)n=amn.
3312⋅2⋅52+13⋅(12)
Combine 12 and 2.
3322⋅52+13⋅(12)
Cancel the common factor of 2.
Cancel the common factor.
3322⋅52+13⋅(12)
Divide 1 by 1.
331⋅52+13⋅(12)
331⋅52+13⋅(12)
Evaluate the exponent.
33⋅52+13⋅(12)
33⋅52+13⋅(12)
33⋅52+13⋅(12)
Multiply 33⋅52.
Multiply 33 and 52.
353⋅2+13⋅(12)
Combine using the product rule for radicals.
3⋅53⋅2+13⋅(12)
Multiply 3 by 5.
153⋅2+13⋅(12)
Multiply 3 by 2.
156+13⋅(12)
156+13⋅(12)
Multiply 13 by 33.
156+13⋅33⋅12
Combine and simplify the denominator.
Multiply 13 and 33.
156+333⋅12
Raise 3 to the power of 1.
156+3313⋅12
Raise 3 to the power of 1.
156+33131⋅12
Use the power rule aman=am+n to combine exponents.
156+331+1⋅12
156+332⋅12
Rewrite 32 as 3.
Use axn=axn to rewrite 3 as 312.
156+3(312)2⋅12
Apply the power rule and multiply exponents, (am)n=amn.
156+3312⋅2⋅12
Combine 12 and 2.
156+3322⋅12
Cancel the common factor of 2.
Cancel the common factor.
156+3322⋅12
Divide 1 by 1.
156+331⋅12
156+331⋅12
Evaluate the exponent.
156+33⋅12
156+33⋅12
156+33⋅12
Multiply 33⋅12.
Multiply 33 and 12.
156+33⋅2
Multiply 3 by 2.
156+36
156+36
The result can be shown in multiple forms.
Exact Form:
156+36
Decimal Form:
0.93417235…
Simplify 1/( square root of 3)*(( square root of 5)/2)+1/( square root of 3)*(1/2)

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