Respuesta :
What is Irrational Number?
An Irrational number is areal number that cannot be expressed as a ratio of integers; for example [tex]\sqrt{2}[/tex] is an irrational number. We cannot express any irrational number in the form of ratio, such as p/q, where p and q are integers, q[tex]\neq[/tex] 0. Again, the decimal expansion of an irrational number in neither terminating nor recurring.
Let us assume [tex]7\sqrt{56}[/tex] is rational.
So, we can write this number as
[tex]7\sqrt{56}[/tex] = a/b __(1)
Here, a and b are two co-prime numbers and b is not equal to zero.
Simplify the equation (1) divide by 7 both sides, we get
[tex]\sqrt{56}=\frac{a}{7b}[/tex]
Here, a and b are integers, so a/7b is a rational number, so [tex]\sqrt{56}[/tex] should be a rational number.
But [tex]\sqrt{56}[/tex] is a irrational number, so it is Contradictory.
Therefore, [tex]7\sqrt{56}[/tex] is irrational number.
Learn more about Rational and Irrational Number at :
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