# Solve for M M=30/( square root of 12+ square root of 27+ square root of 75) M=3012+27+75
Simplify the denominator.
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
Cancel the common factor of 30 and 10.
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
Combine and simplify the denominator.
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 of 3.
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)

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