SOLUTION: Two times the square root of the sum of 3 consecutive even numbers is 24. Find the three numbers.

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Question 656745: Two times the square root of the sum of 3 consecutive even numbers is 24. Find the three numbers.
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 
Hi,
3 consecutive even numbers:
x
x+2
x+4
Two times the square root of the sum of 3 consecutive even numbers is 24
Question states***
2sqrt%283x%2B6%29+=+24
sqrt%283x%2B6%29+=+12 || Squaring both Sides of the EQ
3x+ 6 = 144
3x = 138
x = 46 , 3 consecutive even numbers are: 46, 48, 50
And...
2sqrt%28144%29+=+24

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3consecutive even numbers would be x, x%2B2, and x%2B4
Two times the square root of the sum of 3 consecutive even numbers is 24:

the sum of 3 consecutive even numbers is: x%2B%28x%2B2%29%2B%28x%2B4%29...->...3x%2B6
two times the square root of the sum is 24: 2%2Asqrt%283x%2B6%29=24

2%2Asqrt%283x%2B6%29=24...solve for x
cross%282%29%2Asqrt%283x%2B6%29=cross%2824%2912
sqrt%283x%2B6%29=12....both sides raise to power of two
%28sqrt%283x%2B6%29%29%5E2=12%5E2
3x%2B6=144
3x=144-6
3x=138
highlight%28x=46%29...first number

highlight%28x%2B2=48%29.....second number

highlight%28x%2B4=50%29......third number