Question

Square root of 9680 by prim factoriqsation method

Answer 1

Answer:

2 x 2 x 2 x 2 x 5 x 11 x 11

Answer 2

$\large\underline{\sf{Solution-}}$

$\sf{ \: \sqrt{9680}}$

Let evaluate the Prime factorization of 9680.

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:9680 \:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:4840 \:\:}} \\\underline{\sf{2}}&\underline{\sf{\:\:2420\:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:1210 \:\:}} \\ {\underline{\sf{5}}}& \underline{\sf{\:\:605\:\:}}\\ {\underline{\sf{11}}}& \underline{\sf{\:\:121\:\:}}\\ {\underline{\sf{11}}}& \underline{\sf{\:\:11\:\:}}\\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

So, Prime Factorization of

$\sf{ \: 9680 = {2}^{4} \times {11}^{2} \times 5}$

Therefore,

$\sf \: \sqrt{9680}$

$\rm \: = \: \sqrt{ {2}^{4} \times {11}^{2} \times 5}$

$\rm \: = \: {2}^{2} \times 11 \sqrt{5}$

$\rm \: = \: 44 \sqrt{5}$