Question

Find the square root of $729$ by prime factorisation method

Answer 1

Solve for the square root of given number:

Given number is $729$

By using the Prime factorization method, we get,

$$\begin{gathered} 729=3\times 243 \\ =3\times 3\times 81 \\ =3\times 3\times 3\times 27 \\ =3\times 3\times 3\times 3\times 9 \\ =3\times 3\times 3\times 3\times 3\times 3 \end{gathered}$$

$\therefore 729=3\times 3\times 3\times 3\times 3\times 3=3^6$

Applying square root on both sides,

$\sqrt{729}=\sqrt{3\times 3\times 3\times 3\times 3\times 3}$

$=3\times 3\times 3$

$=27$

$\therefore \sqrt{729}=27$

Hence, the square root of $729$ by using the prime factorization method is $27$.