# Evaluate ( square root of 9/2)^2+6^2

(92)2+62
Simplify each term.
Rewrite 92 as 92.
(92)2+62
Simplify the numerator.
Rewrite 9 as 32.
(322)2+62
Pull terms out from under the radical, assuming positive real numbers.
(32)2+62
(32)2+62
Multiply 32 by 22.
(32⋅22)2+62
Combine and simplify the denominator.
Multiply 32 and 22.
(3222)2+62
Raise 2 to the power of 1.
(32212)2+62
Raise 2 to the power of 1.
(322121)2+62
Use the power rule aman=am+n to combine exponents.
(3221+1)2+62
(3222)2+62
Rewrite 22 as 2.
Use axn=axn to rewrite 2 as 212.
(32(212)2)2+62
Apply the power rule and multiply exponents, (am)n=amn.
(32212⋅2)2+62
Combine 12 and 2.
(32222)2+62
Cancel the common factor of 2.
Cancel the common factor.
(32222)2+62
Divide 1 by 1.
(3221)2+62
(3221)2+62
Evaluate the exponent.
(322)2+62
(322)2+62
(322)2+62
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to 322.
(32)222+62
Apply the product rule to 32.
322222+62
322222+62
Simplify the numerator.
Raise 3 to the power of 2.
92222+62
Rewrite 22 as 2.
Use axn=axn to rewrite 2 as 212.
9(212)222+62
Apply the power rule and multiply exponents, (am)n=amn.
9⋅212⋅222+62
Combine 12 and 2.
9⋅22222+62
Cancel the common factor of 2.
Cancel the common factor.
9⋅22222+62
Divide 1 by 1.
9⋅2122+62
9⋅2122+62
Evaluate the exponent.
9⋅222+62
9⋅222+62
9⋅222+62
Raise 2 to the power of 2.
9⋅24+62
Multiply 9 by 2.
184+62
Cancel the common factor of 18 and 4.
Factor 2 out of 18.
2(9)4+62
Cancel the common factors.
Factor 2 out of 4.
2⋅92⋅2+62
Cancel the common factor.
2⋅92⋅2+62
Rewrite the expression.
92+62
92+62
92+62
Raise 6 to the power of 2.
92+36
92+36
To write 36 as a fraction with a common denominator, multiply by 22.
92+36⋅22
Combine 36 and 22.
92+36⋅22
Combine the numerators over the common denominator.
9+36⋅22
Simplify the numerator.
Multiply 36 by 2.
9+722
812
812
The result can be shown in multiple forms.
Exact Form:
812
Decimal Form:
40.5
Mixed Number Form:
4012
Evaluate ( square root of 9/2)^2+6^2

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