Square Root of 10 using Prime Factorization
When expressed as a product of its primes, 10 can be written as: 2 × 5
Hence, √10 = √(2 × 5)
When we calculate the square root of a perfect square number, we simply take one value out of the two repeated ones and multiply them to get an answer.
However, in the case of 10, we can’t pick any such pairs. Thus, the most that we can do is express the square root of 10 as √(2 × 5).
Hence, the value of square root using prime factorization is given as: √10 = √2 × √5
Now,
- √2 = 1.414..
- √ 5 = 2.236…
Hence, √10 = √(2 × 5) = 1.414.. × 2.236… = 3.162…
Also Check, Prime Factorization
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Square Root of 10 is 3.16227766. It is represented as √10 or 101/2. Square Root of a number is the number that when multiplied by itself gives the original number which is called the Square of the Square Root number.
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