What is the square root of 41.7 and 0.6781, and 0.8?

1 Answer
Mar 17, 2018

Answer:

#sqrt(41.7)~~ 6.4576#
#sqrt(0.6781) ~~0.8196#
#sqrt(0.8) ~~0.89443#

Explanation:

Given: Find the square root of 41.7, 0.6781 and 0.8

If you use a calculator:
#sqrt(41.7)~~ 6.4576#
#sqrt(0.6781) ~~0.8196#
#sqrt(0.8) ~~0.89443#

To find a square root without a calculator takes some time.
For example, hopefully you know that the #sqrt(36) = 6# and the #sqrt(49) = 7#.

Since #36 < 41.7 < 49#, you would know that the #sqrt(41.7)# is between #6# and #7#.

If you take the difference between 41.7 and 36 & 49 and 41.7, you would see that 41.7 is closer to 36. This would mean the #sqrt(41.7) is less than 6.5.

#6.5^2 = 42.25#
#6.4^2 = 40.96#

This means #sqrt(41.7) ~~6.4...#

#6.45^2 = 41.6025#

As you can see we are getting closer to #41.7#. We need a number slightly larger.

Try #6.455^2 = 41.667025#

As you can see we are getting closer to #41.7#

Try #6.456^2 = 41.679936#

Try #6.457^2 = 41.692849#

Try #6.458^2 = 41.705764#

Because #6.457^2 < 41.7 < 6.458^2# We would have to add another decimal to #6.457# to approach #41.7#

Try #6.4575^2 = 41.69930625#

This process can be very tedious, but works.