Question

Find the square root of 0.065 correct to three places of decimal.

Answer 1

	0.2549
2	0.06500000  04
45	250 225
504	2500 2016
5089	48400 45801
	2599

`sqrt0.065`

Write 0.065 as 65×10⁻³. Using the property of square roots:

`sqrt0.065 = sqrt (65xx10^-3) = sqrt65.sqrt(10^-3)`

`sqrt(10^-3) = 10^-3/2 = 10^-1.5 = 0.0316`

Approximate `sqrt 65`

The square root of 65 is approximately 8.062.

Multiply the results

`sqrt 0.065 = sqrt65.sqrt(10^-3)`

= 8.062⋅0.0316

= 0.255