0%2B%20%20%5Csqrt%7B6%7D%20%2B%20..........%20%20%5C%3A%20to%20%5C%3A%20%20%5Cinfin%20%7D%20%20%7D%20%20%5C%3A%20is%20%5C%3A%20%20%5Cunderline%7B%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20.%7D" id="TexFormula1" title="The \: value \: of \: \sqrt{6 + \sqrt{6 + \sqrt{6} + .......... \: to \: \infin } } \: is \: \underline{ \: \: \: \: \: \: \: \: \: \: \: .}" alt="The \: value \: of \: \sqrt{6 + \sqrt{6 + \sqrt{6} + .......... \: to \: \infin } } \: is \: \underline{ \: \: \: \: \: \: \: \: \: \: \: .}" align="absmiddle" class="latex-formula">
CORRECT EXPLANATION WILL BE MARK AS BRAINLIEST.
1 answer:

<u>Let us assume that:</u>

We can also write it as:

Squaring both sides, we get:


By splitting the middle term:



<u>Therefore:</u>


<u>But x cannot be negative. </u>

Therefore, the value of the expression is 3.

Given:

We can also write it as:






This pattern will continue.

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Hope this helped!
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Step-by-step explanation:
Givens
Formula
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Answer:
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Step-by-step explanation:
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