Question
Radical 1,225 in simplest form
Answers
GPT-4o mini
To simplify the square root of 1,225, we first find the prime factorization of 1,225.
1,225 can be factored as follows:
- It is divisible by 5: \(1,225 \div 5 = 245\)
- 245 can also be divided by 5: \(245 \div 5 = 49\)
- 49 is \(7 \times 7\) or \(7^2\).
Now we can express 1,225 as:
\[ 1,225 = 5^2 \times 7^2 \]
To find the square root, we take the square root of each factor:
\[
\sqrt{1,225} = \sqrt{5^2 \times 7^2} = \sqrt{5^2} \times \sqrt{7^2} = 5 \times 7 = 35
\]
Thus, the simplest form of \(\sqrt{1,225}\) is:
\[
\boxed{35}
\]
1,225 can be factored as follows:
- It is divisible by 5: \(1,225 \div 5 = 245\)
- 245 can also be divided by 5: \(245 \div 5 = 49\)
- 49 is \(7 \times 7\) or \(7^2\).
Now we can express 1,225 as:
\[ 1,225 = 5^2 \times 7^2 \]
To find the square root, we take the square root of each factor:
\[
\sqrt{1,225} = \sqrt{5^2 \times 7^2} = \sqrt{5^2} \times \sqrt{7^2} = 5 \times 7 = 35
\]
Thus, the simplest form of \(\sqrt{1,225}\) is:
\[
\boxed{35}
\]