find square root of 2304 by long division method and verify the result by prime factorisation
Answers
Answer:
48
Step-by-step explanation:2304/2=1152
1152/2=576
576/2=288
288/2=144
144/2=72
72/2=36
36/2=18
18/2=9
9/3=3
3/3=1
2304 is a multiple of eight 2s and Two 3s.
Now make it into two groups (four 2s and one 3 in each group)
2304= (2*2*2*2*3)(2*2*2*2*3)
=48*48
Therefore, square root of 2304 is 48.
ANOTHER METHOD IS..DIVIDING METHOD BY CONSIDERING TWO DIGITS AT A TIME FROM RIGHT SIDE. AS EVEN NUMBER OF DIGITS ARE THERE, IT WILL BE LIKE 23, 04. (IF IT IS IN ODD NUMBERS OF DIGITS LIKE 12304, THEN IT SHOULD BE 1,23,04).
NOW first divide 23 by the nearest square root
23/4=4 and remainder will be 7,04
I.e. 2304/4 (to divide first digits only) gives remainder 7 in font of which you put next two digits 04 to get 704.
Then,
704/10(4+4)+x
704/80+X. Choose X such that when (80+X) is multiplied by X you get 704. In this case assuming 2304 is perfect square, to get 4 in one's place either X should be 2 or 8. If you put 2 it will be 82*2=164, hence 2 is ruled out. Now put X=8. Then it will be 704.
Hence, 704/88*8=704/704 gives you remainder zero.
Now the dividers 4 and 8 are to placed in 10th place and one's place to get 48.
48 is the square root of 2304.