Question

find the square root of 734 by prime factorization

Answer 1

1) To be able to simplify the square root of 734, one of the factors of 734 other than 1 must be a perfect square. The factors of 734 are 1, 2, 367, and 734. Since none of these factors are perfect squares, the square root of 734 cannot be simplified.

2) To be able to simplify the square root of 734, all the prime factors of 734 cannot be unique. When we did prime factorization of 734, we found that 2 x 367 equals 734. Since all the prime factors are unique, the square root of 734 cannot be simplified.