Question

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

${5}^{4} \times {7}^{2} \\ \\ {2}^{6} \times {11}^{10}$

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