Question

35. Show that (√5+ √3 is an irrational number, given that positive square root of 15 is an
irrational number.​

Answer 1

Step-by-step explanation:

It is given that,  \sqrt{15}15  is an irrational number,

⇒ \sqrt{5\times 3}5×3 is an irrational number,

⇒ \sqrt{5} \times \sqrt{3}5×3 is an irrational number,

⇒ \sqrt{5}5 and  \sqrt{3}3 are irrational numbers,

⇒ \sqrt{5}+\sqrt{3}5+3  is an irrational number. ( Because, sum of two irrational number is also irrational number)

Hence, proved.

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