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Find square root of $1225$ using prime factorisation.

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Relationship between squares and square roots

Full solution

Q. Find square root of

1225

using prime factorisation.

Find Prime Factors: First, let's find the prime factors of $1225$ . $1225$ can be divided by $5$ , so $1225 = 5 \times 245$ .
Divide and Factorize: Now, let's divide $245$ by $5$ again. $\newline$ $245 = 5 \times 49$ .
Identify Perfect Square: Next, we see that $49$ is a perfect square, which is $7 \times 7$ . So, we can write $1225$ as $5 \times 5 \times 7 \times 7$ .
Calculate Square Root: To find the square root, we pair the prime factors. $\newline$ The square root of $1225$ is $\sqrt{(5 \times 5 \times 7 \times 7)} = 5 \times 7$ .
Final Result: Therefore, the square root of $1225$ is $35$ .

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