MATHS COMIC STRIP
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- Hello, thanks for meeting me here for the preparation of the Real Numbers test happening in school.
- Hi, there is no reason, this was a great idea because if we have any questions we can help each other
- Okay so let's get started and recapitulate the real numbers. Can you tell me how to find LCM and HCF using Prime Factorization ?
- Yes, HCF is the product of the smallest power of each common prime factor of the given numbers E.g. HCF of 240 and 360240= 2*2*2*2*3*5=2^4*3*5360=2*2*2*3*3*5=2^3*3^2*5HCF=2^3*3*5 Now can you tell me how to find LCM using Prime Factorization
- Yes, LCM is the product of the grreatest power of each prime factor of the given numbers E.g. LCM of 240 and 360240 = 2*2*2*2*3*5=2^4*3*5360=2*2*2*3*3*5=2^3*3^2*5LCM= 2^4*3^2*5=720
- What is the relationship between HCF and LCM of two numbers ?
- HCF is always the factor of the LCM of two numbers. If 'a' and 'b' are two numbers, then HCF (a,b) * LCM (a,b) = Product of 'a' and 'b'.
- Can you give me a example ?
- For two numbers 24 and 36Prime factorization of 24 = 2^3*3 and 36=2^2*3^2HCF=2^2*3=12LCM=2^3*3^2=72HCF*LCM=PRODUCT OF TWO NUMBERS12*72=24*36864=864
- Nice ! looks like you've been doing a lot of practice lately now can you tell me how to prove root 2 irrational ?
- No I don't know how to prove root 2 as Irrational can you tell me how to prove it Irrational ?
- (root 2)^2= (p)^2 (by theorem 1.3)let r be any integer then 2r=p (sq. both sides)4r^2=p^2 by simplifying 2r^2=q^2 (by theorem 1.3 ) since 5 is a factor our assumption was wrong Hence root 2 is Irrational
- Yes, First we've to assume root 2 as Rational number.Then, root 2 =p/q (since rational numbers are in the form of p/q where p and q are integers and q unequal to 0. After that root 2q=p (by sq. both sides)
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