Find x.

X^2/ 1.2 =5.62X10^-5
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1 Answer

x2/1.2=5.62×10-5, x2=6.744×10-5=67.44×10-6, x=8.2122×10-3=0.0082122 approx.

To find √67.44 using a form of division:

Write 67.44 as 67.44 00 00 00.

Nearest square to 67 is 64=82, so write 8 above 67:

   8.

 67.44 00 00 00

-64

  3 44

Now multiply 8 by 20=160 and divide approximately into 344. 344/160 is approximately 2, so add 2 to 160=162 and write 2 next to 8 in the answer.

Now multiply 162 by 2=324 and subtract from 344:

   8.  2

 67.44 00 00 00

-64

  3 44

 -3 24

     20 00

Next, multiply 82 by 20=1640. This divides into 2000 just once, so 1640+1=1641 and subtract from 2000 and write 1 next to 2 in the answer:

   8.  2   1

 67.44 00 00 00

-64

  3 44

 -3 24

     20 00

   -16 41

      3 59 00

20×821=16420; 35900/16420=2 (approx); 16420+2=16422:

   8.  2  1   2

 67.44 00 00 00

-64

  3 44

 -3 24

     20 00

    -16 41

       3 59 00

      -3 28 44

         30 56 00

20×8212=164240. This divides into 305600 only once so the next subtrahend is 164241. However 2×164241=328482 which is closer to 305600, and we can round off the next decimal as 2: 

   8.  2  1   2   2

 67.44 00 00 00

-64

  3 44

 -3 24

     20 00

    -16 41

       3 59 00

      -3 28 44

         30 56 00

         16 42 41

           4 13 59 ...

The process continues indefinitely because the square root is irrational.

Finally we need the square root of 10-6=10-3 (or 0.001). Hence the square root 8.2122×10-3.

by Top Rated User (1.2m points)

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