Question

if the sum S of three consecutive even numbers is a perfect square between 200 and 400 then the square root of S is ​

Answer 1

hey mate

here is the answer...

let the number be x,x+2 and x+4.

so,

S=x+x+2+x+4 = 3x+6=3(x+2)

i.e, even number (as the sum of 3 even numbers is even).so S should be even and multiple of 3.

so, the even perfect square number between 200 and 400 are 256 (16)² and 324 (18)².

but from the above calculation,S should be multiple of 3.

256 is not multiple of 3 but 324 is the multiple of 3.

so,S is equal to 324.

and hence the square root of 324 is 18 (answer).

Answer 2

Answer:

18

Step-by-step explanation:

let the number be x,x+2 and x+4.

so,

S=x+x+2+x+4 = 3x+6=3(x+2)

i.e, even number (as the sum of 3 even numbers is even).so S should be even and multiple of 3.

so, the even perfect square number between 200 and 400 are 256 (16)² and 324 (18)².

but from the above calculation,S should be multiple of 3.

256 is not multiple of 3 but 324 is the multiple of 3.

so,S is equal to 324.

and hence the square root of 324 is 18 (answer).

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