Question

What is the smallest number that 45 can be multiplied by to give a perfect square?

Answer 1

use trial and error.

Answer 2

Is there a better way?

Answer 3

yes, there's a way.

Answer 4

can you factor 45 ?

Answer 5

@Sepeario ?

Answer 6

ok, to get a perfect square, we need pairs of numbers,
like 49=7*7, pair of 7.
100 = 10*10 = 2*2* 5*5 , pairs of 2 and 5.
similarly, if you want a perfect square, you just have to complete squares,
say for example you have 28.
first you factor 28 = 2*2*7
now you see, that 2 is forming a pair, but 7 doesn't.
so, the smallest number which you have to multiply to 28 is = 7 to make it perfect square,
(because 2*2*7*7 is a perfect square of 2*7=14)
can you do the same thing with 45 ?

Answer 7

@hartnn Thanks.

Answer 8

so which number will you multiply ?

Answer 9

5

Answer 10

the smallest PERFECT square is 1 right ?
1^2 = 1

in the question, we are asked the smallest real no. which when multiplied by 45 yields a perfect sq,
so , shouldnt ans be 1/45 ? ;)

i know that shouldnt be correct, but the asked hasnt put up a decent language to the question, and so,,why not play! :D

Answer 11

asker*

Answer 12

@shubhamsrg , 0 is a perfect square , isn't it ?
so, smallest number---->0
smallest natural number---->5

Answer 13

0 is a very imp number :)

Answer 14

ahh yep..0 !!

Answer 15

First factor 45It needs just one 5 more to make a pair of two equal numbers so the smallest number is 5.