Question

√2116=46 then the value of √21.16+√0.2116+√0.002116? ​​​

Answer 1

Given:-

• $\sf \sqrt{2116} = 46$

To find:-

• $\sf \sqrt{21.16} + \sqrt{0.2116} + \sqrt{0.002116}$

Answer:-

$\sf \sqrt{21.16} + \sqrt{0.2116} + \sqrt{0.002116}$

$\sf \longrightarrow \: \sqrt{ \dfrac{2116}{100} } + \sqrt{ \dfrac{2116}{10000} } + \sqrt{ \dfrac{2116}{1000000} }$

$\sf \longrightarrow \: \dfrac{ \sqrt{2116} }{ \sqrt{100} } + \dfrac{ \sqrt{2116} }{ \sqrt{10000} } + \dfrac{ \sqrt{2116} }{ \sqrt{1000000} }$

$\sf \longrightarrow \: \dfrac{ \sqrt{2116} }{ \sqrt{ {10}^{2} } } + \dfrac{ \sqrt{2116} }{ \sqrt{ {100}^{2} } } + \dfrac{ \sqrt{2116} }{ \sqrt{ {1000}^{2} } }$

$\sf \longrightarrow \: \dfrac{ \sqrt{2116} }{10} + \dfrac{ \sqrt{2116} }{100} + \dfrac{ \sqrt{2116} }{1000}$

Putting $\sf \sqrt{2116} = 46 ,$

$\sf \longrightarrow \: \dfrac{46}{10} + \dfrac{46}{100} + \dfrac{46}{1000}$

$\sf \longrightarrow \: 4.6 + 0.46 + 0.046$

$\sf \longrightarrow \: 5.106 \:$

Hence,

$\longrightarrow \small \underline{\underline{\sf{\green{\sqrt{21.16} + \sqrt{0.2116} + \sqrt{0.002116} = 5.106}}}}$