Question

what is the square root of 999996

Answer 1

square root is 999.997999997

Answer 2

hi there!
here's the answer:

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¶ Steps to find square root of Non perfect square x:

• Place the No. x in between the consecutive squares a² < x < b²
=> √x value lies in between a & b
i.e,. a < x < b

• Find No. of Non perfect squares b/w a and b:
Non - perfect squares b/w a and b = 2×a

• Find whether x is nearer to a² or b²
i.e,. find x-a² & b²-x

••• Case-1:
If x-a² is less,
√x = a + [(x-a²)/2a]

••• Case-2:
If b²-x is less,
√x = b - [(b²-x)/2a]

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√999996 = ?

we know,

√1000000 = 1000
& √998001 = 999

• 998001 < 999996 < 1000000
√(998001) < √(999996) < √(1000000)
999 < √(999996) < 1000

¶ No. of Non perfect squares b/w 999 & 1000 = 2× 999 = 1998

999996 - 998001 = 1995
1000000 - 999996 = 4
The no. 999996 is more nearer to 1000² i.e., 1000000

•°• √(999996) = 1000 - (4/1998)
= 1000 - 0.0002
= 999.9998

•°• √(999996) = 999.9998

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Hope it helps