Question

Find the square root of the following with prime factorization method:
1) 400
2) 625
3) 2025
4) 2500
5) 3025
Please help me :((((

Answer 1

❍ 400

First let's find the prime factors 400

• Prime factors of 400 ↷

‎ 2 | 400

‎ 2 | 200

‎ 2 | 100

‎ 2 | 50

‎ ‎ 2 | 25

‎ 5 | 5

‎ | 1

Now ,

$\sqrt{400} = 2 \times 2 \times2 \times 2 \times 5 \times 5$

$\sqrt{400} = (2 \times 2) \times (2 \times 2) \times (5 \times \: 5)$

$\sqrt{400} = 2 \times 2 \times 5$

$\sqrt{400} = 20$

Hence

the square root of 400 is 20

Answers:-

1. 400 ↪ 20
2. 625 ↪ 25
3. 2025 ↪ 45
4. 2500 ↪ 50
5. 3025 ↪ 55

$\small\bf\fbox\green{Note:}$

Please do refer to the attachments above

$\small\bf\purple{Hope\:it\:helps\:uh\::)}$