Math, asked by priyanka973, 3 months ago

prove that 8+root 5 is irrational

Answers

Answered by charanyagarla

Let us assume that 8+√5 is a rational number.

Since, it is a rational number it can be written in the form of p/q

Therefore,

8+√5 = p/q

√5 = ( p-8q)/q

Now, let's compare the LHS and RHS

LHS is √5 which is an irrational number

RHS is (p-8q)/q which is a rational number

Conclusion:

since LHS and RHS are not equal our assumption is wrong. Therefore 8+√5 is an irrational number.

Hence proved

Answered by SaYwHyDudE

Answer:

SO just replace 2 with 5

√2 is an irrational number

Suppose it can be written in the form of p/q, and q is not equal to zero.

When p and q are relative prime numbers

√2= p/q~~eq(1)

Where p and q are relative prime number

Taking square on both sides of eq(1)

2=p2/q2

Splitting q2 in two terms

2=p2/q.q

Now, taking one q on other side

2q=p2/q~~eq(2)

Since p and q being relative prime number, q cannot divide p and p2.

As l.h.s of eq(2) is an integer i.e; na

Hence, l.h.s of eq(2) is not equal to r.h.s.

Hence, out assumption is wrong.

So, it is proved that √2 is an irrational number.

Get it

Step-by-step explanation:

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