Question

using prime factorization find the square root of the following if possible 99225
answer fast​

Answer 1

$\large\bf\underline {To \: find:-}$

using prime factorisation we need find the square root of 99225 .

$\huge\bf\underline{Solution:-}$

Prime factorisation of 99225:-

$\begin{array}{r|l}3&99225\\\cline{2-2}3&33075 \\ \cline{2 - 2}3&11025 \\ \cline{2 - 2}3&3675 \\ \cline{2 - 2}5&1225\\ \cline{2 - 2}5&245\\ \cline{2 - 2}7&49\\ \cline{2 - 2}7&7 \\ \cline{2 - 2}&1$

So,

$\rm \: 99225 = \underbrace{ 3 \times 3} \times\underbrace{ 3 \times 3 }\times\underbrace{ 5 \times 5} \times\underbrace{ 7 \times 7}$

Now,

Square root of √99225

⠀⠀⠀⠀⠀= √3×3×3×3×5×5×7×7

»» √99225 = 3 × 3 × 5 × 7

»» √99225 = 315

Hence square root of 99225 by using prime factorisation is 315.

Answer 2

Prime factorisation of 99225:-

Now,

Square root of √99225

⠀⠀⠀⠀⠀= √3×3×3×3×5×5×7×7

»» √99225 = 3 × 3 × 5 × 7

»» √99225 = 315

Hence square root of 99225 by using prime factorisation is 315.