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Prove that 6-3√15 is a rational number |
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Answer» Let us assume that 6-3√15 is rational. THEREFORE, we can write it in the FORM of p/q. Here, p & q are co- prime and q ≠ 0. ⟹ 6 -3√15 = p/q ⟹ -3√15 = p/q - 6 ⟹ √15 = (p-6q)/-3Q ⟹ √15 = (6q-p)/3q As p & q both are INTEGER..... Therefore, (6q-p)/3q is a rational number. But √15 is a irrational number. ✰We KNOW that, a rational number can never be equal to irrational number. ☞ Hence, √15 ≠ (6q-p)/3q ✰So, our contradiction is wrong & 6 -3√15 is not a rational number. ☞ It’s an irrational number. Hence, ( proved) |
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