Question

square root of the following numbers by using prime factorization method 5184, 15625​

Answer 1

5184

$</p><p></p><p>\sqrt{5184} = \sqrt{ 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 }</p><p></p><p>\\</p><p>\\</p><p></p><p>\sqrt{5184} = \sqrt[\cancel{2}]{ 2^{\cancel{2}} \times 2^{\cancel{2}} \times 2^{\cancel{2}} \times 3^{\cancel{2}} \times 3^{\cancel{2}} }</p><p></p><p>\\ \\</p><p></p><p>\sqrt{5184} = 2 \times 2 \times 2 \times 3 \times 3</p><p></p><p>\\ \\</p><p></p><p>\sqrt{5184} = 8 \times 9</p><p></p><p>\\ \\ </p><p></p><p>\sqrt{5184} = 72</p><p></p><p>\\ </p><p></p><p>$

15625

$</p><p></p><p>\sqrt{15625} = \sqrt{ 5 \times 5 \times 5 \times 5 \times 5 \times 5}</p><p></p><p>\\ \\</p><p></p><p>\sqrt{15625} = \sqrt[\cancel{2}]{5^{\cancel{2}} \times 5^{\cancel{2}} \times 5^{\cancel{2}} } </p><p></p><p>\\ \\</p><p></p><p>\sqrt{15625} = 5 \times 5 \times 5</p><p></p><p>\\ \\</p><p></p><p>\sqrt{15625} = 125</p><p></p><p>$