What is the solution to the equation 1 over the square root of 8 = 4 (m + 2)

Solve for m:

1/sqrt (8) = 4 (m + 2)

Rationalize the denominator. 1/sqrt (8) = 1/sqrt (8) * (8^ (1 - 1/2)) / (8^ (1 - 1/2)) = (8^ (1 - 1/2)) / 8:

(8^ (1 - 1/2)) / 8 = 4 (m + 2)

Combine powers. (8^ (1 - 1/2)) / 8 = 8^ ((1 - 1/2) - 1):

8^ ((1 - 1/2) - 1) = 4 (m + 2)

Put 1 - 1/2 over the common denominator 2. 1 - 1/2 = 2/2 - 1/2:

8^ (2/2 - 1/2 - 1) = 4 (m + 2)

2/2 - 1/2 = (2 - 1) / 2:

8^ ((2 - 1) / 2 - 1) = 4 (m + 2)

2 - 1 = 1:

8^ (1/2 - 1) = 4 (m + 2)

Put 1/2 - 1 over the common denominator 2. 1/2 - 1 = 1/2 - 2/2:

8^ (1/2 - 2/2) = 4 (m + 2)

1/2 - 2/2 = (1 - 2) / 2:

8^ ((1 - 2) / 2) = 4 (m + 2)

1 - 2 = - 1:

8^ ((-1) / 2) = 4 (m + 2)

1/sqrt (8) = 1/sqrt (2^3) = (1/sqrt (2)) / 2:

(1/sqrt (2)) / 2 = 4 (m + 2)

Rationalize the denominator. 1 / (2 sqrt (2)) = 1 / (2 sqrt (2)) * (sqrt (2)) / (sqrt (2)) = (sqrt (2)) / (2*2) : (sqrt (2)) / (2*2) = 4 (m + 2)

2*2 = 4:

(sqrt (2)) / 4 = 4 (m + 2)

(sqrt (2)) / 4 = 4 (m + 2) is equivalent to 4 (m + 2) = (sqrt (2)) / 4:

4 (m + 2) = sqrt (2) / 4

Expand out terms of the left hand side:

4 m + 8 = sqrt (2) / 4

Subtract 8 from both sides:

4 m + (8 - 8) = (sqrt (2)) / 4 - 8

8 - 8 = 0:

4 m = (sqrt (2)) / 4 - 8

Put each term in (sqrt (2)) / 4 - 8 over the common denominator 4: (sqrt (2)) / 4 - 8 = (sqrt (2)) / 4 - 32/4:

4 m = (sqrt (2)) / 4 - 32/4

(sqrt (2)) / 4 - 32/4 = (sqrt (2) - 32) / 4:

4 m = (sqrt (2) - 32) / 4

Divide both sides by 4:

Answer: m = (sqrt (2) - 32) / (4*4)