Question

Pls give the correct value of the expression:​

Answer 1

★ Solution :

$\sqrt{1+23\sqrt{1+24\sqrt{1+25\sqrt{26 \times 28 + 1}}}}\\ \\ \\ by \: dmas \\ \\ \\ \sqrt{1+23\sqrt{1+24\sqrt{1+25\sqrt{728 + 1}}}}$

$\sqrt{1+23\sqrt{1+24\sqrt{1+25\sqrt{729}}}}\\ \\ \\ 729 = 27 \times 27 \\ \\ \\ \sqrt{1+23\sqrt{1+24\sqrt{1+25 \times 27}}$

$= \sqrt{1+23\sqrt{1+24\sqrt{1+ 675}}}\\ \\ \\ = \sqrt{1+23\sqrt{1+24\sqrt{676}}$

$676 = 26 \times 26 \\ \\ \\ = \sqrt{1+23\sqrt{1+24 \times 26}}$

$= \sqrt{1+23\sqrt{1+624}}\\ \\ \\ = \sqrt{1+23\sqrt{625}} \\ \\ \\ = \sqrt{1+23 \times 25} \\ \\ \\ = \sqrt{1+575} \\ \\ \\ = \sqrt{576}$

${\pink{\boxed{\sqrt{1+23\sqrt{1+24\sqrt{1+25\sqrt{26 \times 28 + 1}}}} = 24}}}$

Answer 2

$\sf\blue{Question}$

$\sf{To \ find \ the \ value \ of}$

$\sf{\sqrt{1+23\sqrt{1+24\sqrt{1+25\sqrt{26\times28+1}}}}}$

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ value \ of}$

$\sf{\sqrt{1+23\sqrt{1+24\sqrt{1+25\sqrt{26\times28+1}}}}}$

$\sf{is \ 24.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{\leadsto{\sqrt{1+23\sqrt{1+24\sqrt{1+25\sqrt{26\times28+1}}}}}}$

$\sf{\leadsto{\sqrt{1+23\sqrt{1+24\sqrt{1+25\sqrt{729}}}}}}$

$\sf{\leadsto{\sqrt{1+23\sqrt{1+24\sqrt{1+25\times27}}}}}$

$\sf{\leadsto{\sqrt{1+23\sqrt{1+24\sqrt{676}}}}}$

$\sf{\leadsto{\sqrt{1+23\sqrt{1+24\times26}}}}$

$\sf{\leadsto{\sqrt{1+23\sqrt{625}}}}$

$\sf{\leadsto{\sqrt{1+23\times25}}}$

$\sf{\leadsto{\sqrt{576}}}$

$\sf{\leadsto{24}}$

$\sf\purple{\tt{\therefore{The \ value \ of}}}$

$\sf\purple{\tt{\sqrt{1+23\sqrt{1+24\sqrt{1+25\sqrt{26\times28+1}}}}}}$

$\sf\purple{\tt{is \ 24.}}$