Question

prove that 2 + 5 root 3 is an irrational number

Answer 1

Hey mate here is your answer

Let, us assume that 2+5√3 is a rational number.

Therefore, 2+5√3=a/b (where a and b are co prime)
5√3=a/b-2
5√3=a-2b/b
√3=a-2b/5b
Therefore, a-2b/5b is in the form of a/b which is rational number.
But,this is contradicts the fact is that √3 is irrational number.
Therefore, our assumption is wrong and 2+5√3 is an irrational number.

Hope this will help you...!!!

Answer 2

Answer:

2 + 5$\sqrt{3}$ is an irrational number. (proved)

Step-by-step explanation:

As per the data given in the question

we have to prove that 2 + 5$\sqrt{3}$ is an irrational number

As per the question it is given that 2 + 5$\sqrt{3}$

Irrational number is the real numbers which cannot be expressed in the form of $\frac{p}{q}$ ,where p and  q are integers and q$\neq$0

Let us assume that 2 + 5$\sqrt{3}$ is a rational number.

Therefore, 2 + 5$\sqrt{3}$ = $\frac{p}{q}$  (p and q are co prime)

so, 5$\sqrt{3}$=$\frac{p}{q}-2$

$\sqrt{3}=\frac{p-2q}{5q}$ , it is in the form of $\frac{p}{q}$ which is rational number.

But here $\sqrt{3}$ is irrational number.

Hence, our assume is wrong and 2 + 5$\sqrt{3}$ is an irrational number.

For such type of question:

https://brainly.in/question/18626352

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