5100+54

Cancel the common factor of 5 and 100.

Factor 5 out of 5.

5(1)100+54

Cancel the common factors.

Factor 5 out of 100.

5⋅15⋅20+54

Cancel the common factor.

5⋅15⋅20+54

Rewrite the expression.

120+54

120+54

120+54

Rewrite 120 as 120.

120+54

Any root of 1 is 1.

120+54

Simplify the denominator.

Rewrite 20 as 22⋅5.

Factor 4 out of 20.

14(5)+54

Rewrite 4 as 22.

122⋅5+54

122⋅5+54

Pull terms out from under the radical.

125+54

125+54

Multiply 125 by 55.

125⋅55+54

Combine and simplify the denominator.

Multiply 125 and 55.

5255+54

Move 5.

52(55)+54

Raise 5 to the power of 1.

52(515)+54

Raise 5 to the power of 1.

52(5151)+54

Use the power rule aman=am+n to combine exponents.

5251+1+54

Add 1 and 1.

5252+54

Rewrite 52 as 5.

Use axn=axn to rewrite 5 as 512.

52(512)2+54

Apply the power rule and multiply exponents, (am)n=amn.

52⋅512⋅2+54

Combine 12 and 2.

52⋅522+54

Cancel the common factor of 2.

Cancel the common factor.

52⋅522+54

Divide 1 by 1.

52⋅51+54

52⋅51+54

Evaluate the exponent.

52⋅5+54

52⋅5+54

52⋅5+54

Multiply 2 by 5.

510+54

Rewrite 54 as 54.

510+54

Simplify the denominator.

Rewrite 4 as 22.

510+522

Pull terms out from under the radical, assuming positive real numbers.

510+52

510+52

510+52

To write 52 as a fraction with a common denominator, multiply by 55.

510+52⋅55

Multiply 52 and 55.

510+5⋅52⋅5

Multiply 2 by 5.

510+5⋅510

510+5⋅510

Combine the numerators over the common denominator.

5+5⋅510

Move 5 to the left of 5.

5+5⋅510

Add 5 and 55.

6510

6510

Factor 2 out of 65.

2(35)10

Cancel the common factors.

Factor 2 out of 10.

2(35)2(5)

Cancel the common factor.

2(35)2⋅5

Rewrite the expression.

355

355

355

The result can be shown in multiple forms.

Exact Form:

355

Decimal Form:

1.34164078…

Evaluate square root of 5/100+ square root of 5/4