Question

root 5 -3-2 is a rational number or not

Answer 1

Answer:

Yes

Step-by-step explanation:

root 5-3-2

root 5-5

0

therefore 0 is not a irrational it is rational no.

Answer 2

Find whether √5 -3 - 2 is a rational number or not.

Given,

√5-3-2

= √5 - 5

To find,

Whether √5 - 5 is rational or not

Solution,

Let us assume that √5 - 5 is rational.

Then, √5 - 5 = p/q, where p and q are co-prime integers and q =/ 0.

√5 = (p + 5q) / q

Since p, q and 5 are integers, (p + 5q) / q is a rational number.

Which implies √5 is also a rational number.

But this contradicts the fact that √5 is irrational. So our assumption is wrong.

Therefore, √5 - 5 is an irrational number.

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