Back to the basics:
I know the sqrt of 343 is 7sqrt(7). What I'd like to learn is how we got there. Is there any easy way of finding out 7x7x7=343?

Question

Back to the basics:
I know the sqrt of 343 is 7sqrt(7). What I'd like to learn is how we got there. Is there any easy way of finding out 7x7x7=343?

anonymous · Answer

$$\sqrt{343}=\sqrt{49*7}=\sqrt{49}*\sqrt{7}=7\sqrt{7}$$

phi · Answer

assuming you don't have a calculator, you might want to memorize some of these divisibility rules https://en.wikipedia.org/wiki/Divisibility_rule#Divisibility_rules_for_numbers_1.E2.80.9320 It is also helpful to memorize the first few prime numbers https://en.wikipedia.org/wiki/List_of_prime_numbers#The_first_500_prime_numbers but 343 is not a particular easy number to factor.

phi · Answer

if you know the divisibility rule for 7:   for 343, do 34 - 2*3= 34-6=28
28 is divisible by 7.  once you find 7*49= 343  you should know 47= 7*7