Question

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

Answer 1

`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.