Question

show tha 2+√7 is an irrational number​

Answer 1

Step-by-step explanation:

2+✓7

2+7×7

2+49=51.

51 I'd correct answer

Answer 2

✍️Question:-

$\green\diamondsuit$ Show that $2 + \sqrt{7}$ is an irrational number?

$\rule{300}{1}$

✍️How to solve?

• Firstly show the sum as rational number and then by using the identities of rational number and putting the word equation solve the question.finallt we are done with the answer.
• ☀️So lets start .

✍️Answer:-

$\tt Let \:\: 2 + \sqrt{7} \:\: be\:\: rational\\\\ \tt \therefore we \:\: can\:\: find\:\: two\:\: integers\\ a, b (b \neq 0) \:\: \tt such\:\: that\\\\ \therefore 2 + \sqrt{7} = \dfrac{a}{b} \\ \tt \therefore \sqrt{7} = \dfrac{a}{b} - 2 \\\\ \tt \implies Since\:\: a \: and \: b \:\: are\:\: integers\:\: \dfrac{a}{b} - 2 \\ \tt is \:\:also \:\: rational\:\: \\ \tt and\:\: hence,\:\: \sqrt{7}\:\: should\:\: be\:\: rational.\\\\ \tt \implies This\:\: contradicts\:\: the\:\: fact\:\: that\\ \tt \sqrt{7} \:\: is\:\: irrational.\\\\ \tt \therefore,\:\: our\:\: assumption\:\: is\:\: false\:\: and\\ \tt hence\:\: 2 + \sqrt{7} \\ \tt is\:\: irrational.$

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☃️Hence, we are done with the problem.