1.

Prove root3 is irrational​

Answer»

\huge \purple {Answer}

Let √3 is a RATIONAL number.

Therefore, It can be expressed in the FORM of p/q, where p and q are co-primes and q≠ 0.

⇒ √3 = \frac {p}{q}

By squaring both sides

⇒ 3 = \frac {p²}{q²}

⇒ 3q² = p² -(i)

This means that 3 divides p². This means that 3 divides p because each factor should appear two times for the SQUARE to exist.

So, we have p = 3r, where r is some integer.

⇒ p² = 9r² -(ii)

from equation (i) and (ii)

⇒ 3q² = 9r²

⇒ q² = 3r²

Where q² is multiply of 3 and also q is MULTIPLE of 3.

Then p, q have a common factor of 3. This runs contrary to their being co-primes. CONSEQUENTLY, \frac {p}{q} is not a rational number. This demonstrates that √3 is an irrational number.

\boxed {Hence, \: proved}


Discussion

No Comment Found

Related InterviewSolutions