Q. 73.7( 6 Votes )
The HCF and LCM o
Let LCM and HCF of the two numbers be X and Y respectively and let a and b be the two numbers.
According to the given criteria, X = 360 and Y = 9
There is an important formula to remember,
LCM (two numbers) × HCF (two numbers) = Product of two numbers.
Now substituting the corresponding values, we get
X × Y = a × b
⇒ 360 × 9 = a × b
⇒ a × b = 3240
But given one number is 45, so let a = 45, we get
⇒ 45 × b = 3240
⇒ b = 72
Hence the other number is 72.
Given: √5 is irrational
To show: 7 − √5 is irrational
Explanation: we will prove this by contradiction method.
So, let us assume 7 − √5 is rational.
And we know a rational number can be written in form, where a and b are co prime (i.e., a and b have no common factor other than 1) and also b≠0, so
Since, a and b are integers.
7b - a will also be an integer.
Hence is rational from our assumption.
But given √5 is irrational
So, from equation (i), irrational = rational
But this is not possible, hence this is a contradiction.
So, our assumption is incorrect.
Therefore 7 – √5 is irrational.
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