SOLUTION: What is the solution to the equation 1 over the square root of 8 = 4(m + 2)? m = −15 over 4 m = −11 over 4 m = 5 over 4 m = 9 over 4

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Question 862276: What is the solution to the equation 1 over the square root of 8 = 4(m + 2)?
m = −15 over 4
m = −11 over 4
m = 5 over 4
m = 9 over 4
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
None of your solutions solves that equation.
1%2Fsqrt%288%29=4%28m%2B2%29
1%2F%282%2Asqrt%282%29%29=4%28m%2B2%29
1%2F%288%2Asqrt%282%29%29=m%2B2
m=1%2F%288%2Asqrt%282%29%29-2
m=sqrt%282%29%2F16-2

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i do not get any of these answers.
equation is:
1/sqrt(8) = 4(m+2)
commute this equation to get:
4(m+2) = 1/sqrt(8)
multiply both sides of this equation by 1/4 to get:
m+2 = 1/4sqrt(8)
subtract 2 from both sides of this equation to get:
m = 1/4sqrt(8) - 2
the decimal equivalent of this is m = -1.911611652...
this is not a rational number because sqrt(8) is not a rational number.
this is the answer, however, because, if you replace m with this number, the original equation will be true.
4(m+2) becomes 4(-1.911611652... + 2) which becomes 4(.088388348...) which becomes .353553391... which is equivalent to the fraction of 1/sqrt(8).
to confirm that, set up the equation of .353553391 = x/sqrt(8) and solve for x to get x = 1.
this means that .353553391 is equivalent to 1/sqrt(8), confirming the original equation is true which confirms that the solution of m = -1.911611652... is good.
the ... at the end of the decimal equivalent means there are more fractional digits than the calculator can display.
i used the stored number from the calculator to derive the final solution.
this stored number carries out the fractional digits to at least 12 decimal places, possibly more.