# Divide (1/( square root of (2)+5))/(5(2)+4)

1(2)+55(2)+4
Multiply the numerator by the reciprocal of the denominator.
1(2)+5⋅15(2)+4
17⋅15(2)+4
Multiply 17 by 77.
17⋅7715(2)+4
Combine and simplify the denominator.
Multiply 17 and 77.
777⋅15(2)+4
Raise 7 to the power of 1.
7717⋅15(2)+4
Raise 7 to the power of 1.
77171⋅15(2)+4
Use the power rule aman=am+n to combine exponents.
771+1⋅15(2)+4
772⋅15(2)+4
Rewrite 72 as 7.
Use axn=axn to rewrite 7 as 712.
7(712)2⋅15(2)+4
Apply the power rule and multiply exponents, (am)n=amn.
7712⋅2⋅15(2)+4
Combine 12 and 2.
7722⋅15(2)+4
Cancel the common factor of 2.
Cancel the common factor.
7722⋅15(2)+4
Divide 1 by 1.
771⋅15(2)+4
771⋅15(2)+4
Evaluate the exponent.
77⋅15(2)+4
77⋅15(2)+4
77⋅15(2)+4
Simplify the denominator.
Multiply 5 by 2.
77⋅110+4
77⋅114
77⋅114
Multiply 77⋅114.
Multiply 77 and 114.
77⋅14
Multiply 7 by 14.
798
798
The result can be shown in multiple forms.
Exact Form:
798
Decimal Form:
0.02699746…
Divide (1/( square root of (2)+5))/(5(2)+4)