Question

We ______ the square root of non-perfect square number.

Answer 1

Let us find the square root of 441. The prime factorization of 441 is 441 = 3 × 3 × 7 × 7. Pairing the prime factors and selecting one from each pair gives 3 × 7 = 21. So, the square root of 441 = √441 = 21.

Let us find the square root of 180. The prime factorization of 180 is 180 = 2 × 2 × 3 × 3 × 5. If we make the pair of the prime factors we see that the prime factor 5 is not in the pair. Therefore 180 is not a perfect square and hence the square root is not perfect. The square root of 180, √180 = 2 × 3 × √5 = 6√5.

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