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Question
Find the square root of 7 correct to two decimal places; then use it to find the value of `sqrt((4+sqrt(7))/(4-sqrt(7)` correct to three significant digits.
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Solution
`sqrt(7)` = 2.645 = 2.65
| 2.645 | |
| 2 | 7.000000 4 |
| 46 | 300 276 |
| 524 | 2400 2096 |
| 5285 | 30400 26425 |
| 3975 |
Now, `sqrt((4+sqrt(7))/(4-sqrt(7)`
= `sqrt(((4+sqrt(7))(4+sqrt7))/((4-sqrt7)(4+sqrt(7))`
= `sqrt(((4+sqrt(7))^2)/((4)^2 - sqrt((7))^2)`
= `sqrt(((4+sqrt(7))^2)/(16-7)`
= `sqrt(((4+sqrt(7))^2)/(9)`
= `(4+sqrt(7))/(3)`
= `(4+2.65)/(3)`
= `(6.65)/(3)`
= 2.21
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