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

5100+54
Simplify each term.
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
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
Write each expression with a common denominator of 10, by multiplying each by an appropriate factor of 1.
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
Simplify the numerator.
Move 5 to the left of 5.
5+5⋅510
6510
6510
Cancel the common factor of 6 and 10.
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

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