Question

If using prime factorization method, we get $\sqrt{\left(2025\right)}=3^2\times k$, then the value of $k$ is equal to:

• A. 45
• B. 3
• C. 9
• D. 5

Answer 1

The correct option is D 5

Given,
$\sqrt{\left(2025\right)}=3^2\times k$ ------(i)

Prime factorization of $2025$ is,
$\begin{array}{cc}3& 2025\\ 3& 675\\ 3& 225\\ 3& 75\\ 5& 25\\ & 5\end{array}$

$\therefore 2025=3\times 3\times 3\times 3\times 5\times 5$

Making pairs of the prime numbers:
$2025=\underset{–}{3\times 3}\times \underset{–}{3\times 3}\times \underset{–}{5\times 5}$

$\Rightarrow \sqrt{\left(2025\right)}=3\times 3\times 5\Rightarrow \sqrt{\left(2025\right)}=3^2\times 5$

From (i) we have,
$\Rightarrow$ $3^2\times k$ $=3^2\times 5$
$\Rightarrow$ $k=$ $5$

$\therefore$ The value of $k$ is $5$.