Question

find the following square roots,using 'prime factors':

i) 784
ii) 7056. 1
iii) 20----
4
please give answers and tell me how to do. please

Answer 1

I do not understand well your question, but:

784 = 2 ∙ 2 ∙ 2 ∙ 2 ∙ 7 ∙ 7 = 2⁴∙ 7²

√784 = √(2⁴∙ 7²) = √2⁴∙ √7² = 2² ∙ 7 = 4 * 7 = 28

7056 = 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3 ∙ 3 ∙7 ∙ 7 = 2⁴∙ 3² ∙7²

√7056 = √(2⁴∙ 3² ∙ 7²) = √2⁴∙ √3² ∙ √7² = 2² ∙ 3 ∙ 7 = 4 * 21 = 84

20 = 4 ∙ 5

√20 = √( 4 ∙ 5) = √4 ∙ √5 = 2 √5