5(10+35)

Apply the distributive property.

510+5(35)

Combine using the product rule for radicals.

5⋅10+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

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)