# Simplify ( square root of 5+ square root of 45)/(3- square root of 20) 5+453-20
Simplify the numerator.
Rewrite 45 as 32⋅5.
Factor 9 out of 45.
5+9(5)3-20
Rewrite 9 as 32.
5+32⋅53-20
5+32⋅53-20
Pull terms out from under the radical.
5+353-20
Add 5 and 35.
453-20
453-20
Simplify the denominator.
Rewrite 20 as 22⋅5.
Factor 4 out of 20.
453-4(5)
Rewrite 4 as 22.
453-22⋅5
453-22⋅5
Pull terms out from under the radical.
453-(25)
Multiply 2 by -1.
453-25
453-25
Multiply 453-25 by 3+253+25.
453-25⋅3+253+25
Multiply 453-25 and 3+253+25.
45(3+25)(3-25)(3+25)
Expand the denominator using the FOIL method.
45(3+25)9+65-65-452
Simplify.
45(3+25)-11
Group 3+25 and 5 together.
4((3+25)5)-11
Apply the distributive property.
4(35+255)-11
Multiply 255.
Raise 5 to the power of 1.
4(35+2(515))-11
Raise 5 to the power of 1.
4(35+2(5151))-11
Use the power rule aman=am+n to combine exponents.
4(35+251+1)-11
Add 1 and 1.
4(35+252)-11
4(35+252)-11
Simplify each term.
Rewrite 52 as 5.
Use axn=axn to rewrite 5 as 512.
4(35+2(512)2)-11
Apply the power rule and multiply exponents, (am)n=amn.
4(35+2⋅512⋅2)-11
Combine 12 and 2.
4(35+2⋅522)-11
Cancel the common factor of 2.
Cancel the common factor.
4(35+2⋅522)-11
Divide 1 by 1.
4(35+2⋅51)-11
4(35+2⋅51)-11
Evaluate the exponent.
4(35+2⋅5)-11
4(35+2⋅5)-11
Multiply 2 by 5.
4(35+10)-11
4(35+10)-11
Move the negative in front of the fraction.
-4(35+10)11
The result can be shown in multiple forms.
Exact Form:
-4(35+10)11
Decimal Form:
-6.07571052…
Simplify ( square root of 5+ square root of 45)/(3- square root of 20)

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