Question

3 MARKS QUESTION EACH :

Q1.Prove that 5+213 is irrational.

Q2.Given that HCF (112,256) = 16, find LCM (112,256).

Please solve Both!!
Request!!!

​

Answer 1

Q1. 5+213 is rational not irrational

Q2. LCM(112,256)=1792

Answer 2

Answer:

Step-by-step explanation:

1. Let us assume,to the contrary, that 5+2√3 is rational so it can be written in the form 5+2√3=a / b where a and b are co-prime.Now,

=> 5+2√3 = a / b

=> 2√3 = a / b -5

=> 2√3 = a-5b / b

=> √3 = a-5b / b × 1 / 2

=> √3 = a-5b / 2b

Here a, b, 2 and 5 are all rational number so a-5b / 2b is a rational number so √3 is irrational

But this contradicts the fact that √3 is irrational.

This contradiction has arisen because of our incorrect assumption, that 5+2√3 is rational.

So, 5+2√3 is irrational.

2. HCF(112,256)=16

LCM(112,256)=?

We know,

LCM × HCF = PRODUCT OF TWO NUMBERS

=> LCM × 16 = 112 ×256

=> LCM = 112 × 256 / 16

=> LCM = 1792

Therefore, LCM(112,256) = 1792