M=3012+27+75

Rewrite 12 as 22⋅3.

Factor 4 out of 12.

M=304(3)+27+75

Rewrite 4 as 22.

M=3022⋅3+27+75

M=3022⋅3+27+75

Pull terms out from under the radical.

M=3023+27+75

Rewrite 27 as 32⋅3.

Factor 9 out of 27.

M=3023+9(3)+75

Rewrite 9 as 32.

M=3023+32⋅3+75

M=3023+32⋅3+75

Pull terms out from under the radical.

M=3023+33+75

Rewrite 75 as 52⋅3.

Factor 25 out of 75.

M=3023+33+25(3)

Rewrite 25 as 52.

M=3023+33+52⋅3

M=3023+33+52⋅3

Pull terms out from under the radical.

M=3023+33+53

Add 23 and 33.

M=3053+53

Add 53 and 53.

M=30103

M=30103

Factor 10 out of 30.

M=10⋅3103

Cancel the common factors.

Factor 10 out of 103.

M=10⋅310(3)

Cancel the common factor.

M=10⋅3103

Rewrite the expression.

M=33

M=33

M=33

Multiply 33 by 33.

M=33⋅33

Multiply 33 and 33.

M=3333

Raise 3 to the power of 1.

M=33313

Raise 3 to the power of 1.

M=333131

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

M=3331+1

Add 1 and 1.

M=3332

Rewrite 32 as 3.

Use axn=axn to rewrite 3 as 312.

M=33(312)2

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

M=33312⋅2

Combine 12 and 2.

M=33322

Cancel the common factor of 2.

Cancel the common factor.

M=33322

Divide 1 by 1.

M=3331

M=3331

Evaluate the exponent.

M=333

M=333

M=333

Cancel the common factor.

M=333

Divide 3 by 1.

M=3

M=3

The result can be shown in multiple forms.

Exact Form:

M=3

Decimal Form:

M=1.73205080…

Solve for M M=30/( square root of 12+ square root of 27+ square root of 75)