Question

1.
Find the square root of each of the following by prime factorisation.
(i) 225
(ii) 441
(iii) 529
(iv)
40000
(V) 7744
(vi)
8281
(vii)
4096
(viii)
28900​

Answer 1

Answer:

i. 15, ii. 21, iii. 23, iv. 200, v. 88, vi. 91, vii. 64, viii. 170. I hope it will help you.

Answer 2

Before, finding the answer. Let's find out how we can find the answer.

• Here, we have to find the Square Root of each number by Prime factorisation method.
• So, to find that we must divide the number by the prime numbers.
• Then, we have to multiply all the numbers. And that is the Square Root.

__________________

⇒ Question :

→ Find the square root of each of the following by prime factorisation.

(i) 225

$\Large{ \begin{array}{c|c} \sf 5 & \sf{ 225 } \\ \cline{1-2} \sf 5 & \sf {45 } \\ \cline{1-2} \sf 3 & \sf{ 9 \\ \cline{1-2} \sf 3 & \sf{3} \\ \cline{1-2} \sf & \sf{ 1} \end{array}}$

225 = 5² × 3²

        = 5 × 3

       = 15

(ii) 441

$\Large{ \begin{array}{c|c} \sf 3 & \sf{ 441} \\ \cline{1-2} \sf 3 & \sf {147} \\ \cline{1-2} \sf 7 & \sf{ 49} \\ \cline{1-2} \sf 7 & \sf{ 7} \\ \cline{1-2} \sf & \sf{ 1 } \end{array}}$

441 = 3² × 7²

Square Root = 3 × 7

          = 21

(iii) 529

$\Large{ \begin{array}{c|c} \sf 23 & \sf{529} \\ \cline{1-2} \sf 23 & \sf {23} \\ \cline{1-2} \sf & \sf{ 1} \end{array}}$

Square root = 23

(iv)  40000

$\Large{ \begin{array}{c|c} \sf 5 & \sf{ 40000} \\ \cline{1-2} \sf 5 & \sf {8000} \\ \cline{1-2} \sf 5 & \sf{ 1600} \\ \cline{1-2} \sf 5 & \sf{ 320 } \\ \cline{1-2} \sf 2 & \sf {64} \\ \cline{1-2} \sf 2 & \sf{ 32} \\ \cline{1-2} \sf 2 & \sf {16 } \\ \cline{1-2} \sf 2 & \sf {8} \\ \cline{1-2} \sf 2 & \sf {4} \\ \cline{1-2} \sf 2 & \sf {2} \\ \cline{1-2} \sf & \sf {1}\end{array}}$

Square Root = 5² × 5² × 2² × 2² × 2²

                     = 5 × 5 × 2 × 2 × 2

                     = 200

(v) 7744

$\Large{ \begin{array}{c|c} \sf 2 & \sf{7744} \\ \cline{1-2} \sf 2 & \sf {3872} \\ \cline{1-2} \sf 2 & \sf{1936} \\ \cline{1-2} \sf 2 & \sf{968} \\ \cline{1-2} \sf 2 & \sf {484} \\ \cline{1-2} \sf 2 & \sf{ 242} \\ \cline{1-2} \sf 11 & \sf {121} \\ \cline{1-2} \sf 11 & \sf {11} \\ \cline{1-2} \sf & \sf {1} {1}\end{array}}$

Square Root = 2² × 2² × 2² × 11² × 11²

                     = 2 × 2 × 2 × 11 × 11

                     = 88

(vi)  8281

$\Large{ \begin{array}{c|c} \sf 7 & \sf{8281} \\ \cline{1-2} \sf 7 & \sf {1183} \\ \cline{1-2} \sf 13 & \sf{ 169} \\ \cline{1-2} \sf 13 & \sf{13} \\ \cline{1-2} \sf & \sf{ 1 } \end{array}}$

Square Root = 7² × 7² × 13² × 13²

                     = 7 × 13

                     = 91

(vii)  4096

$\Large{ \begin{array}{c|c} \sf 2 & \sf{ 4096} \\ \cline{1-2} \sf 2 & \sf {2048} \\ \cline{1-2} \sf 2 & \sf{ 1024} \\ \cline{1-2} \sf 2 & \sf{ 512} \\ \cline{1-2} \sf 2 & \sf {256} \\ \cline{1-2} \sf 2 & \sf{128} \\ \cline{1-2} \sf 2 & \sf {64} \\ \cline{1-2} \sf 2 & \sf {32} \\ \cline{1-2} \sf 2 & \sf {16} \\ \cline{1-2} \sf 2 & \sf {8} \\ \cline{1-2} \sf 2& \sf {4} \\ \cline{1-2}2 \sf & \sf {2} \\ \cline{1-2} \sf & \sf {1} \end{array}}$

Square Root = 2² × 2² × 2² × 2² × 2² × 2²

                     = 2 × 2 × 2 × 2 × 2 × 2

                     = 64

(viii)  28900​

$\Large{ \begin{array}{c|c} \sf 2 & \sf{ 28900 } \\ \cline{1-2} \sf 2 & \sf {14450 } \\ \cline{1-2} \sf 5 & \sf{ 2890} \\ \cline{1-2} \sf 5 & \sf{578} \\ \cline{1-2} \sf 17 \sf & \sf{ 34} \\ \cline{1-2} \sf 2 & \sf{ 2} \\ \cline{1-2} \sf & \sf{ 1} \end{array}}$

Square Root = 2² × 5² × 17²

                     = 2 × 5 × 17

                     = 170