Question

Find the square roots of 441 and 1521 by the Prime Factorisation Method.

Answer 1

Let us find the square root of 441 first.


441 = 3×3×7×7
441 = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $3^2$ × <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $7^2$
441 = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${(3\times 7)}^2$
441 = ${21}^2$
Therefore, <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\sqrt{441}$ = 21

Now, let us find the square root of 1521


1521 = 3×3×13×13
1521 = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $3^2$ × <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${13}^2$
1521 = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${(3\times 13)}^2$
1521 = ${39}^2$
Therefore, <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\sqrt{1521}$ = 39