Question

Find the square root.
(i) 625 (ii) 1225 (iii) 289 (iv) 4096 (v) 1089

Answer 1

(i) The prime factorization of 625 is,
625 = 5 × 5 × 5 × 5
To find the square root, we will take one number from each pair and multiply.
$$\begin{gathered} \sqrt{625}=5\times 5=25 \\ \therefore \sqrt{625}=25 \end{gathered}$$
(ii) The prime factorization of 1225 is,
1225 = 5 × 5 × 7 × 7
To find the square root, we will take one number from each pair and multiply.
$$\begin{gathered} \sqrt{1225}=5\times 7=35 \\ \therefore \sqrt{1225}=35 \end{gathered}$$
(iii) The prime factorisation of 289 is,
289 = 17 × 17
To find the square root, we will take one number from each pair and multiply.
$$\begin{gathered} \sqrt{289}=17\times 17=17 \\ \therefore \sqrt{289}=17 \end{gathered}$$
(iv) The prime factorization of 4096 is,
4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 ​× 2
To find the square root, we will take one number from each pair and multiply.
$$\begin{gathered} \sqrt{4096}=2\times 2\times 2\times 2\times 2\times 2=64 \\ \therefore \sqrt{4096}=64 \end{gathered}$$
(v) The prime factorizationn of 1089 is,
1089 = 3 × 3 × 11 × 11
To find the square root, we will take one number from each pair and multipy.
$$\begin{gathered} \sqrt{1089}=3\times 11=33 \\ \therefore \sqrt{1089}=33 \end{gathered}$$