# Simplify square root of 5( square root of 10+3 square root of 5) 5(10+35)
Apply the distributive property.
510+5(35)
Combine using the product rule for radicals.
5⋅10+5(35)
Multiply 5(35).
Raise 5 to the power of 1.
5⋅10+3(515)
Raise 5 to the power of 1.
5⋅10+3(5151)
Use the power rule aman=am+n to combine exponents.
5⋅10+351+1
Add 1 and 1.
5⋅10+352
5⋅10+352
Simplify each term.
Multiply 5 by 10.
50+352
Rewrite 50 as 52⋅2.
Factor 25 out of 50.
25(2)+352
Rewrite 25 as 52.
52⋅2+352
52⋅2+352
Pull terms out from under the radical.
52+352
Rewrite 52 as 5.
Use axn=axn to rewrite 5 as 512.
52+3(512)2
Apply the power rule and multiply exponents, (am)n=amn.
52+3⋅512⋅2
Combine 12 and 2.
52+3⋅522
Cancel the common factor of 2.
Cancel the common factor.
52+3⋅522
Divide 1 by 1.
52+3⋅51
52+3⋅51
Evaluate the exponent.
52+3⋅5
52+3⋅5
Multiply 3 by 5.
52+15
52+15
The result can be shown in multiple forms.
Exact Form:
52+15
Decimal Form:
22.07106781…
Simplify square root of 5( square root of 10+3 square root of 5)

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