Advertisements
Advertisements
Question
If `sqrt(2) = 1.4142`, then `sqrt((sqrt(2) - 1)/(sqrt(2) + 1))` is equal to ______.
Options
2.4142
5.8282
0.4142
0.1718
Solution
If `sqrt(2) = 1.4142`, then `sqrt((sqrt(2) - 1)/(sqrt(2) + 1))` is equal to 0.4142.
Explanation:
`sqrt((sqrt(2) - 1)/(sqrt(2) + 1)) = sqrt((sqrt(2) - 1)/(sqrt(2) + 1) xx (sqrt(2) - 1)/(sqrt(2) - 1))`
= `sqrt((sqrt(2) - 1)^2/((sqrt(2))^2 - 1^2)`
= `sqrt((sqrt(2) - 1)^2/(2 - 1)`
= `sqrt((sqrt(2) - 1)^2/1`
= 1.4142 – 1
= 0.4142
APPEARS IN
RELATED QUESTIONS
Write the following in decimal form and say what kind of decimal expansion has:
`36/100`
You know that `1/7=0.bar142857.` Can you predict what the decimal expansions of `2/7, 3/7, 4/7, 5/7, 6/7` are, Without actually doing the long division? If so, how?
[Hint: Study the remainders while finding the value of `1/7` carefully.]
Express 0.99999 .... in the form `p/q`. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of `1/17`? Perform the division to check your answer.
Look at several examples of rational numbers in the form `p/q` (q≠0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?
`2sqrt(3) + sqrt(3)` is equal to ______.
There are numbers which cannot be written in the form `p/q, q ≠ 0, p, q` both are integers.
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
0.2555...
Show that 0.142857142857... = `1/7`
Write the following in decimal form and say what kind of decimal expansion has:
`329/400`
