Question

how to find square root using prime factorisation

Answer 1

I explain it with an example:
Find the square root of 441 in prime factorisation method:

Step I: write the prime factorisation of 441
441= 3×3×7×7
Step II: From each pair of equal factors occuring in the prime factorisation, take one of the factors and write the product of these factors. The product so obtained is the square root of the given number.
Thus, √441=√(3×3)×(7×7) = 3×7=21