Question

Find the positive square roots of the following numbers, giving your answers in prime factorization form


`{5}^(4) * {7}^(2) \\ \\ {2}^(6) * {11}^(10)`

Answer 1

Hello from MrBillDoesMath!

Answer:

prime factorization of sqrt( 5^4 x 7^2) = (5^2) *7

prime factorization of sqrt(2^6 x 11^10) = (2^3) * (11^5)

Discussion:

sqrt( 5^4 x 7^2) = 5^2 * 7 => as 5 and 7 are prime numbers

prime factorization = 5^2 *7

sqrt(2^6 x 11^10) = 2^3 * 11^5 => as 2 and 11 are prime numbers

prime factorization = 2^3 * 11^5

Thank you,

MrB