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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.
Solution
`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
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