# Simplify square root of (5/8-9/16)÷(1+9/16)

(58-916)÷(1+916)
To write 58 as a fraction with a common denominator, multiply by 22.
58⋅22-9161+916
Write each expression with a common denominator of 16, by multiplying each by an appropriate factor of 1.
Multiply 58 and 22.
5⋅28⋅2-9161+916
Multiply 8 by 2.
5⋅216-9161+916
5⋅216-9161+916
Combine the numerators over the common denominator.
5⋅2-9161+916
Simplify the numerator.
Multiply 5 by 2.
10-9161+916
Subtract 9 from 10.
1161+916
1161+916
Write 1 as a fraction with a common denominator.
1161616+916
Combine the numerators over the common denominator.
11616+916
1162516
Multiply the numerator by the reciprocal of the denominator.
116⋅1625
Cancel the common factor of 16.
Cancel the common factor.
116⋅1625
Rewrite the expression.
125
125
Rewrite 125 as 125.
125
Any root of 1 is 1.
125
Simplify the denominator.
Rewrite 25 as 52.
152
Pull terms out from under the radical, assuming positive real numbers.
15
15
The result can be shown in multiple forms.
Exact Form:
15
Decimal Form:
0.2
Simplify square root of (5/8-9/16)÷(1+9/16)

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