Question

Prove that 9 - √15 is an irrational number.​

Answer 1

Step-by-step explanation:

yes this is irrational numbers

Answer 2

Let, us assume that 9-√15 is an irrational number then we can write in the for form of p/q, where p and q are co-primes and q is not equal to 0

$\orange{9-√15 = \dfrac{p}{q}}$

$\orange{\dfrac{9 \times q}{1 \times q}-\dfrac{p}{q} = √15}$

$\orange{\dfrac{9q - p}{q} = √15}$

$Therefore, \orange{\dfrac{9q-0}{q}} \: is \: an \: rational \: number$

$But \: we\: know \: that \: √15 \: is \: an \: irrational \: number$

$From \: this \: our \: assumption \: is \: wrong$

$Hence, \orange{9-√15}\: is \: not \: an \: rational \: number$

$Hence, \orange{9-√15} \: is \: an \: irrational \: number$

[Hope this helps you.../]