Question

Find the square root of the following (correct to three decimal place) 7​

Answer 1

Given Question :-

Find the square root of 7 correct to three decimal places

$\green{\large\underline{\bf{Solution-}}}$

$\purple{\bf :\longmapsto\: \sqrt{7}}$

Using long division,

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:2.645 \:\:}}}\\ {\underline{\sf{2}}}& {\sf{\:\:7.000000 \:\:}} \\{\sf{}}& \underline{\sf{\:\:4 \: \: \: \: \: \: \: \: \: \: \: \:\:}} \\ {\underline{\sf{46}}}& {\sf{\:\:300 \: \: \: \: \: \: \: \:\:}} \\{\sf{}}& \underline{\sf{\:\:276 \: \: \: \: \: \: \:\:}} \\ {\underline{\sf{524}}}& {\sf{\:\:2400 \:\:}} \\{\sf{}}& \underline{\sf{\:\:2096\:\:}} \\ {\underline{\sf{5285}}}& {\sf{\:\: \: \: \: \: \: \: 30400\:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: \: 26425\:\:}} \\ {\underline{\sf{}}}& {\sf{\: \: \: \: \: \: \: \: \: \: \: 3975\:\:}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}\end{gathered}\end{gathered}$

Hence,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underbrace{ \boxed{ \bf \: \sqrt{7} = 2.645}}$

Additional Information :-

Irrational numbers :-

• Numbers whom decimal representation are non terminating and non repeating are called Irrational numbers. Basically, the square root of non - perfect square numbers are irrational. For example :- √2, √3, √5, --- etc.

Rational Numbers :-

• Numbers whom decimal representation are terminating and non - terminating but repeating are called rational numbers. For example :- 2, 1/2, 1/3, --- etc.