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Question

1. The square root of 4,356 is an integer. Without a calculator, determine what the integer is by eliminating possibilities. Do the same for 8464.

Answer 1

4356 is divisible by 9 and 4 and by 36. add up the digits, they sum to 18 any even number is divisible by 2

4356/4 = 1089

1089/9 = 121

121/11 = 11

4356 = 4x9x11

sqr4356 = sqr(4)(9)(121 = 2(3)(11) = 66

or 4356 = 36(121) = 6^2(11^2)

sqr5356 = 6(11) = 66

8464 is divisible by 4

8464/4 = 2116 which is also divisible by 4 (look at the last 2 digits, 16 is divisible by 4)

2116/4 = 529

25 squared = 625

20 squared = 400

sqr529 is in between20 and 26, you need to end in 9, 3^2 = 9. try 23

8464 = 4^2(23)^2

sqr8464 = 4(23) = 92