Question

show that √(12+2√27) is an irrational number​

Answer 1

Answer:

yes

Step-by-step explanation:

$( \sqrt{12} + 2 \sqrt{27} ) \\ \sqrt{2 \times 2 \times 3} + 2 \sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 13 } \\ \sqrt{2 {}^{2} \times 3 } + 2 \sqrt{2 {}^{2} \times 2 {}^{2} \times 3 \times 13 } \\ \sqrt{2 {}^{2} \times 3 } + 2 \sqrt{2 {}^{2} \times 2 {}^{2} \times 39 } \\ \sqrt{2 {}^{2} } \times \sqrt{3} + 2 \sqrt{2 {}^{2} } \times \sqrt{2 {}^{2} } \times \sqrt{39} \\ 2 \times \sqrt{3} + 4 \times 2 \times \sqrt{39} \\ \sqrt{6} + 8 \times \sqrt{39} \\ \sqrt{6} \times 8 \sqrt{39}$

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