Question

prove that root 3 is irrational​

Answer 1

Let us assume that √3 is a rational number.

then, as we know a rational number should be in the form of m/n

where m and n are co- prime number.

So,

√3 = m/n { where m and n are co- prime}

√3n = m

Now, by squaring both the side

we get,

(√3m)² = m²

3n² = m² ........ ( 1 )

So,

if 3 is the factor of m²

then, 3 is also a factor of m ..... ( 2 )

=> Let m = 3p { where p is any integer }

squaring both sides

m² = (3p)²

m² = 9p²

putting the value of m² in equation ( 1 )

3n² = m²

3n² = 9p²

n² = 3p²

So,

if 3 is factor of n²

then, 3 is also factor of n

Since

3 is factor of m & n both

So, our assumption that m & n are co- prime is wrong

hence,. √3 is an irrational number

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Answer 2

Answer:

Step-by-step explanation: