Question

Find the value of `sqrt5` correct to 2 decimal places; then use it to find the square root of `(3-sqrt(5))/(3+sqrt(5)` correct to 2 significant digits.

Answer 1

`sqrt(5)` = 2.236 = 2.24

	2.236
2	5.000000 4
42	100 84
443	1600 1329
4466	27100 26796
	304

 

 

 

 

 

 

 

 

 

 

`(3-sqrt(5))/(3+sqrt(5)`

= `sqrt(((3-sqrt(5))((3-sqrt(5))))/((3+sqrt(5))(3-sqrt(5))`

= `sqrt(((3-sqrt(5))^2)/((3)^2 - sqrt((5))^2)`

= `sqrt((3-sqrt5)^2)/(9-5)`

= `sqrt((3-sqrt(5)^2)/(4)`

= `((3-2.24))/(2)`

= `((0.76))/(2)`

= 0.38