Question

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Answer 1

To Find :-

• Value of

$\sf \sqrt{10+\sqrt{24+\sqrt{131+\sqrt{153+\sqrt{256}}}}}$

Solution :-

$\sf \sqrt{10+\sqrt{24+\sqrt{131+\sqrt{153+\sqrt{256}}}}}$

$:\implies \sf \sqrt{10+\sqrt{24+\sqrt{131+\sqrt{153+16}}}}$

$:\implies \sf \sqrt{10+\sqrt{24+\sqrt{131+\sqrt{169}}}}$

$:\implies \sf \sqrt{10+\sqrt{24+\sqrt{131+13}}}$

$:\implies \sf \sqrt{10+\sqrt{24+\sqrt{144}}}$

$:\implies \sf \sqrt{10+\sqrt{24+12}}$

$:\implies \sf\sqrt{10+\sqrt{36}}$

$:\implies \sf \sqrt{10+6}$

$:\implies \sf \sqrt{16}$

$:\implies{\underline{\boxed{\frak{\purple{ 4}}}}}\;\bigstar$

$\boxed {\sf {\purple {The \ required \ value\ is\ 4}}}$

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Need to Know :-

• $\sf \sqrt {256}= 16$

• $\sf \sqrt{169}= 13$

• $\sf\ \sqrt{144}=12$

• $\sf \ \sqrt{36}= 6$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

$\large\underline\mathfrak\orange{Answer⤵}$

$➡ \sqrt{10 \sqrt{24 \sqrt{131 \sqrt{153 \sqrt{256} } } } }$

$➡ \sqrt{10 \sqrt{24 \sqrt{131 \sqrt{153 + 16} } } }$

$➡ \sqrt{10 \sqrt{24 \sqrt{131 \sqrt{169} } } }$

$➡ \sqrt{10\sqrt{24 \sqrt{131 +13} } }$

$➡ \sqrt{10 \sqrt{24 \sqrt{144} } }$

$➡ \sqrt{10 \sqrt{24 + 12} }$

$➡ \sqrt{10 \sqrt{36} }$

$➡ \sqrt{10 + 6}$

$➡ \sqrt{16}$

$\large\red{\boxed{\sf{Answer=4}}}$