Question

Kindly solve it!..................​

Answer 1

Answer:

4

Step-by-step explanation:

First here some error in question

Last one root value is 225

So,

√[10+√(25+√(108+√(154+√(225))))]

=>

√[10+√(25+√(108+√(154+√(15×15))))]

=>

√[10+√(25+√(108+√(154+15)))]

=>

√[10+√(25+√(108+√(169)))]

=>

√[10+√25+√(108+√(13×13)))]

=>

√[10+√(25+√(108+13))]

=>

√[10+√(25+√(121))]

=>

√[10+√(25+√(11×11))]

=>

√[10+√(25+11)]

=>

√[10+√(36)]

=>

√[10+√(6×6)]

=>

√[10+6]

=>

√16

=>

√(4×4)

=>

Answer =4

Hope it's helpful for you ☺✌

Answer 2

$\large \bf {\underline {\underline {Correct \: question : - } }}$

$\sf \: The \: value \: of \: \sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{154 + \sqrt{225} } } } } \: is$

$\bf {\underline {\underline{ Solution : - }}}$

$\sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{154 + \sqrt{225} } } } } \\ \\ = \sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{154 + 15} } } } \\ \\ = \sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{169} } } } \\ \\ = \sqrt{10 + \sqrt{25 + \sqrt{108 + 13} } } \\ \\ = \sqrt{10 + \sqrt{25 + \sqrt{121} } } \\ \\ = \sqrt{10 + \sqrt{25 + 11} } \\ \\ = \sqrt{10 + \sqrt{36} } \\ \\ = \sqrt{10 + 6} \\ \\ = \sqrt{16} = 4$

$\therefore \: \sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{154 + \sqrt{225} } } } } = 4$

$\bf{ \underline {\underline{ Note : - }}}$

$\longmapsto \: \sqrt{169} = 13 \\ \\ \longmapsto \sqrt{121} = 11 \\ \\ \longmapsto \: \sqrt{36} = 6 \\ \\ \longmapsto \: \sqrt{16} = 4\\ \\ \longmapsto\:\sqrt{225}=15$