Find the square root by factorisation method in 25 and 225
The Correct Answer and Explanation is:
√25 and √225 by Factorisation Method
√25:
Step 1: Factorise 25
25 = 5 × 5
Step 2: Group identical pairs
(5 × 5) → one pair of 5s
Step 3: Take one number from the pair
√25 = 5
√225:
Step 1: Factorise 225
Start by dividing with the smallest prime numbers
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
So, 225 = 3 × 3 × 5 × 5
Step 2: Group identical pairs
(3 × 3) and (5 × 5)
Step 3: Take one number from each pair
√225 = 3 × 5 = 15
Explanation (Approx. 300 Words)
The factorisation method of finding square roots involves expressing a number as a product of its prime factors and then using those factors to find the square root. This method works well for perfect squares, which are numbers that have exact square roots.
For example, 25 is a perfect square because it can be written as 5 multiplied by 5. After breaking it down into prime factors, there is only one pair of 5s. Since the square root of a number is a value that, when multiplied by itself, gives the original number, taking one number from the pair gives the square root. Therefore, √25 equals 5.
For 225, the process starts with prime factorisation. The smallest prime that divides 225 is 3. Dividing successively gives two 3s. The remaining number, 25, is divided further by 5 to give two 5s. So, 225 is written as 3 × 3 × 5 × 5. Here, there are two pairs: one of 3s and one of 5s. Taking one number from each pair and multiplying them gives the square root. That is 3 × 5, which equals 15. So, √225 is 15.
This method is useful because it avoids the use of decimals or guesswork. It is especially effective for numbers that are known or suspected to be perfect squares. For non-perfect squares, other methods like the division method or approximation are preferred.
