Q. 74.8( 5 Votes )

The HCF and LCM o

Answer :

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) = Multiplication 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.


OR


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






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.


Hence 7 - √5 is irrational.


Hence proved


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