Advertisements
Advertisements
प्रश्न
Show that (5 - 2`sqrt(3)`) is irrational.
उत्तर
Let x = 5 - 2`sqrt(3)` be a rational number.
x = 5 - 2`sqrt(3)`
⇒` x^2 = (5 - 2sqrt(3))2`
⇒ `x^2 = 5^2 + (2sqrt(3))^2 – 2(5) (2 sqrt(3) )`
⇒ x2 = 25 + 12 – 20√3
⇒ `x^2 – 37 = – 20sqrt(3)`
⇒`( 37− x^2)/20 =sqrt(3)`
Since x is a rational number, `x^2` is also a rational number.
⇒ 37 -` x^2` is a rational number
⇒ `(37− x^2)/20` is a rational number
⇒`sqrt(3)` is a rational number
But `sqrt(3)` is an irrational number, which is a contradiction.
Hence, our assumption is wrong.
Thus, (5 - 2`sqrt(3)` ) is an irrational number.
APPEARS IN
संबंधित प्रश्न
Give an example of two irrational numbers whose:
difference is a rational number.
Give an example of two irrational numbers whose:
difference is an irrational number.
Give an example of two irrational numbers whose:
sum is an irrational number.
Classify the numbers 1.535335333 as rational or irrational:
Prove that of the numbers ` 2 - sqrt(3)` is irrational:
State whether the given statement is true or false:
1 . The product of a rational and an irrational is irrational .
Write four rational numbers between `sqrt(2) and sqrt(3)`
The product of any two irrational numbers is ______.
Classify the following number as rational or irrational with justification:
`sqrt(9/27)`
Show that the product of a non-zero rational number and an irrational number is an irrational number.
