Question

Find the square root of 17,424 without using calculator or tables

Answer 1

Prime Factors!

Answer 2

hmm try dividing this by 121

Answer 3

with squareroots; divvy it up into pairs of 2 from the decimal like this:

1 74 24 now we can slice and dice it

Answer 4

Wait or would that be considered using a table?

Answer 5

a64 yes that is what I need

Answer 6

what is the closest square that equals "1" ?

Answer 7

by hand, we address x^2 + 2xy + y^2 format

Answer 8

use long division

Answer 9

we need to start with an x^2 that is close to, but not greater then, our target grouping. in this case, its a "1" :)

Answer 10

I would use long division to divide 17,424 by 121 since 121 is 11^2, but i think that would count as memorizing the table

Answer 11

the "by hand" steps weed out any guess work

Answer 12

i c

Answer 13

our first target group in this case is "1"; and we wish to find an "x^2" that is close to or equal to it.

1^2 = 1 ... thats great :)

1-1 = 0; now drop down the next grouping, in this case its 74

0 74 ; the zero is there just for show; lets focus on the 74 part..

this next step is the "tricky" part; we know our x^2, and we gotta find a (2x)y that matches our grouping. ... recall that x=1 in this case

x y
----- ; this is our setup
2xy | 074


?
-----
2(1)__ | 074

1 ?
----- ; twenty "something" times "the unknown" is equal
2__ | 074 to or less then "74"

20*0 = 0
21*1 = 21
22*2 = 44
23*3 = 69
24*4 = 96 .... to big, lets go with 3



1 3
-----
23 | 074
-69
-----
5 ; now attach our next grouping (24) to this and repeat

13 ? ; since x = 13 now, (2x)y is 26__
-----
26__ | 524

260*0 = 0
261*1 = 261
262*2 = 524 .. that one works



13 2 ; since x = 13 now, (2x)y is 26__
-----
262 | 524
524
-----
0

the answer is; 132

Answer 14

Thanks

Answer 15

if any of that doesnt make sense, let me know so I can try to clarify it :)

Answer 16

It does :D

Answer 17

great :)

Answer 18

the cubic are much worse ... and dont even get me started and 4roots lol