find the square root of the following, correct to threee places of decimal of 7​

2 thoughts on “find the square root of the following, correct to threee places of decimal of 7​”

1. Step-by-step explanation:

   We have to find the square root of 7 upto three decimal places. Therefore, we get the square root of 7 up to three decimal places as 2.645. We have to find the square root of 17 upto three decimal places. Therefore, we get the square root of 17 up to three decimal places as 4

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2. [tex]\large\underline{\sf{Solution-}}[/tex]

   ☆ Square root of 7 using long division

   [tex]\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}[/tex]

   [tex]\bf\implies \: \sqrt{7} = 2.645[/tex]

   Additional Information :-

   Let us take few more examples :-

   1. Square root of 2 upto 3 decimal places.

   [tex]\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:1.414 \:\:}}}\\ {\underline{\sf{1}}}& {\sf{\:\:2.000000 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: \: 1 \: \: \: \: \: \: \: \: \: \: \: \:\:}} \\ {\underline{\sf{24}}}& {\sf{\:\: \: \: \: \: 100 \: \: \: \: \: \: \: \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: 96 \: \: \: \: \: \: \:\:}} \\ {\underline{\sf{281}}}& {\sf{\:\:400 \:\:}} \\{\sf{}}& \underline{\sf{\:\:281\:\:}} \\ {\underline{\sf{2824}}}& {\sf{\:\: \: \: \: \: \: 11900\:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: 11296\:\:}} \\ {\underline{\sf{}}}& {\sf{\: \: \: \: \: \: \: \: \: \: \: 604\:\:}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}\end{gathered}\end{gathered}[/tex]

   [tex]\bf\implies \: \sqrt{2} = 1.414[/tex]

   2. Square root of 3 upto 3 decimal places.

   [tex]\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:1.732 \:\:}}}\\ {\underline{\sf{1}}}& {\sf{\:\:3.000000 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: \: \: 1 \: \: \: \: \: \: \: \: \: \: \: \:\:}} \\ {\underline{\sf{27}}}& {\sf{\:\: \: \: \: \: 200 \: \: \: \: \: \: \: \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: 189 \: \: \: \: \: \: \:\:}} \\ {\underline{\sf{343}}}& {\sf{\:\:1100 \:\:}} \\{\sf{}}& \underline{\sf{\:\:1029\:\:}} \\ {\underline{\sf{3462}}}& {\sf{\:\: \: \: \: \: \: 7100\:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: 6924\:\:}} \\ {\underline{\sf{}}}& {\sf{\: \: \: \: \: \: \: 176\:\:}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}\end{gathered}\end{gathered}[/tex]

   [tex]\bf\implies \: \sqrt{3} = 1.732[/tex]

   Important facts :-

   [tex]\rm :\longmapsto\: \sqrt{x \times y} = \sqrt{x} \times \sqrt{y} [/tex]

   [tex]\rm :\longmapsto\: \sqrt{\dfrac{x}{y} } = \dfrac{ \sqrt{x} }{ \sqrt{y} } [/tex]

   [tex]\rm :\longmapsto\: \sqrt{ {x}^{2} } = x[/tex]

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