what is the square root of 625
What is the square root of 625?
The square root of 625 can be found by determining the number that, when multiplied by itself, equals 625. The operation to find the square root can be mathematically represented as:
\sqrt{625}
Let’s break it down step by step:
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First, let’s rewrite 625 as a product of its prime factors if necessary.
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625 is an exact square number, so can be straightforward to find its root:
- 625 = 25 \times 25
- Moreover, 25 = 5 \times 5
- Therefore, 625 = (5 \times 5) \times (5 \times 5) = 5^4
Hence the process can be summarized as:
625 = 5^4
To find the square root, we can take half the power of all the prime factors:
\sqrt{5^4} = 5^{4/2} = 5^2
Simplifying this gives:
5^2 = 25
Therefore, the square root of 625 is:
\sqrt{625} = 25