Advertisements
Advertisements
प्रश्न
Write the following in descending order:
`sqrt(6), root(3)(8) and root(4)(3)`
उत्तर
Since `sqrt(6) = 6^(1/2) "has power" (1)/(2)`,
`root(3)(8) = 2`
`root(4)(3) = 3^(1/4) "has power" (1)/(4)`
Now, L.C.M. of 2, 1 and 4 = 4
∴ `sqrt(6) = 6^(1/2) = 6^(2/4) = (6^2)^(1/4) = (36)^(1/4)`
`root(3)(8) = 2 = 2^(4/4) = (2^4)^(1/4) = (16)^(1/4)`
`root(4)(3) = 3^(1/4) = (3^1)^(1/4) = (3)^(1/12)`
Since, 36 > 16 > 3, we have `(36)^(1/4) > (16)^(1/4) > (3)^(1/12)`.
Hence, `sqrt(6) > root(3)(8) > root(4)(3)`.
APPEARS IN
संबंधित प्रश्न
Prove that 3 + 2`sqrt5` is irrational.
Give an example of two irrational numbers whose:
difference is a rational number.
Classify the numbers 3.121221222 as rational or irrational:
Prove that the following number is irrational: 3 - √2
Insert five irrational numbers between `2sqrt5` and `3sqrt3`.
State whether the following number is rational or irrational
`(5 - sqrt(5))^2`
Show that `sqrt(5)` is an irrational numbers. [Use division method]
Without using division method show that `sqrt(7)` is an irrational numbers.
Write the following in ascending order:
`5sqrt(7), 7sqrt(5) and 6sqrt(2)`
Write two rational numbers between `sqrt(3) and sqrt(7)`
