Answer:
The square root of 3249, (or root 3249), is the number which when multiplied by itself gives the product as 3249. Therefore, the square root of 3249 = √3249 = 57.
Step-by-step explanation:
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[tex] \qquad \: \qquad \boxed{ \sf{ \:\bf \sqrt{3249} = 57 \: \: }}\\ \\ [/tex]
Given number is
[tex] \qquad \: \sqrt{3249} \\ \\ [/tex]
So, using prime factorization method, prime factors of
[tex]\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{3}}}&{\underline{\sf{\:\:3249\:\:}}}\\ {\underline{\sf{3}}}& \underline{\sf{\:\:1083 \:\:}} \\\underline{\sf{19}}&\underline{\sf{\:\:361\:\:}} \\ {\underline{\sf{19}}}& \underline{\sf{\:\:19\:\:}} \\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered} \\ \\ [/tex]
So,
[tex]\sf\implies 3249 = 3 \times 3 \times 19 \times 19 \\ \\ [/tex]
[tex]\sf\implies \sqrt{3249} = \sqrt{3 \times 3 \times 19 \times 19} \\ \\ [/tex]
[tex]\sf\implies \sqrt{3249} = 3 \times 19 \\ \\ [/tex]
[tex]\bf\implies \sqrt{3249} = 57 \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Alternative Method
[tex] \qquad\sf \: \sqrt{3249} \\ \\ [/tex]
Using Long Division Method, we have
[tex]\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{57}}}\\ {\underline{\sf{5}}}& {\sf{3249}} \\{\sf{}}& \underline{\sf{25 \: \: \: \: }} \\ {\underline{\sf{107}}}& {\sf{ \: \: \: 749 }} \\{\sf{}}& \underline{\sf{ \: \: \: 749 }} \\ {\underline{\sf{}}}& {\sf{0}}\end{array}\end{gathered} \\ \\ \\ [/tex]
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Answers & Comments
Answer:
The square root of 3249, (or root 3249), is the number which when multiplied by itself gives the product as 3249. Therefore, the square root of 3249 = √3249 = 57.
Step-by-step explanation:
hope it will help you
mark has brilliant answer
Verified answer
Answer:
[tex] \qquad \: \qquad \boxed{ \sf{ \:\bf \sqrt{3249} = 57 \: \: }}\\ \\ [/tex]
Step-by-step explanation:
Given number is
[tex] \qquad \: \sqrt{3249} \\ \\ [/tex]
So, using prime factorization method, prime factors of
[tex]\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{3}}}&{\underline{\sf{\:\:3249\:\:}}}\\ {\underline{\sf{3}}}& \underline{\sf{\:\:1083 \:\:}} \\\underline{\sf{19}}&\underline{\sf{\:\:361\:\:}} \\ {\underline{\sf{19}}}& \underline{\sf{\:\:19\:\:}} \\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered} \\ \\ [/tex]
So,
[tex]\sf\implies 3249 = 3 \times 3 \times 19 \times 19 \\ \\ [/tex]
[tex]\sf\implies \sqrt{3249} = \sqrt{3 \times 3 \times 19 \times 19} \\ \\ [/tex]
[tex]\sf\implies \sqrt{3249} = 3 \times 19 \\ \\ [/tex]
[tex]\bf\implies \sqrt{3249} = 57 \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Alternative Method
Given number is
[tex] \qquad\sf \: \sqrt{3249} \\ \\ [/tex]
Using Long Division Method, we have
[tex]\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{57}}}\\ {\underline{\sf{5}}}& {\sf{3249}} \\{\sf{}}& \underline{\sf{25 \: \: \: \: }} \\ {\underline{\sf{107}}}& {\sf{ \: \: \: 749 }} \\{\sf{}}& \underline{\sf{ \: \: \: 749 }} \\ {\underline{\sf{}}}& {\sf{0}}\end{array}\end{gathered} \\ \\ \\ [/tex]
So,
[tex]\bf\implies \sqrt{3249} = 57 \\ \\ [/tex]