Answer:
What smallest number should be multiplied to 11664 to make it a perfect cube?
So, you want the smallest umber that, when multiplied by 11664, gives a perfect square.
I note that most people have given 4. But there are better candidates.
How about zero? After all, 0 < 4! 0 times 11664 = 0 = 0 cubed.
Better yet, as Stephen Jones suggested, is -4, as -4 < 0
−4×11664=−46656=(−36)3
Better yet, how about -136,048,896 (= -11,664 times 11,664), which is certainly less than -4.
−136048896×11664=−1×116643=(−11664)3
Better yet, how about -136,048,896,000 (= -116,640 times 116,640 times 10), which is certainly less than -136,048,896
−136048896000×11664=−1×1166403=(−116640)3
We could keeping multiplying our negative number by multiples of 1,000 until the end of time and still we wouldn’t have got to the smallest number
Let’s find all the prime factors of the given number,
11664 = 2 x 5832
11664 = 2 x 2 x 2916
11664 = 2 x 2 x 2 x 1458
11664 = 2 x 2 x 2 x 2 x 729
11664 = 2 x 2 x 2 x 2 x 3 x 243
11664 = 2 x 2 x 2 x 2 x 3 x 3 x 81
Let me jump a few steps here
11664 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
Now we make a Trio of similar numbers as,
11644 = (2 x 2 x 2) x (2) x (3 x 3 x 3) x (3 x 3 x 3)
We can see there is only 1 digit left out.
We can multiply it by a pair of same numbers i.e 2 to make the given number a Perfect Cube.
Thus the number if multiplied by 4 becomes a perfect cube (46656 = 36 x 36 x 36).
hope it helps you friend.......
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Answers & Comments
Answer:
What smallest number should be multiplied to 11664 to make it a perfect cube?
So, you want the smallest umber that, when multiplied by 11664, gives a perfect square.
I note that most people have given 4. But there are better candidates.
How about zero? After all, 0 < 4! 0 times 11664 = 0 = 0 cubed.
Better yet, as Stephen Jones suggested, is -4, as -4 < 0
−4×11664=−46656=(−36)3
Better yet, how about -136,048,896 (= -11,664 times 11,664), which is certainly less than -4.
−136048896×11664=−1×116643=(−11664)3
Better yet, how about -136,048,896,000 (= -116,640 times 116,640 times 10), which is certainly less than -136,048,896
−136048896000×11664=−1×1166403=(−116640)3
We could keeping multiplying our negative number by multiples of 1,000 until the end of time and still we wouldn’t have got to the smallest number
Answer:
Let’s find all the prime factors of the given number,
11664 = 2 x 5832
11664 = 2 x 2 x 2916
11664 = 2 x 2 x 2 x 1458
11664 = 2 x 2 x 2 x 2 x 729
11664 = 2 x 2 x 2 x 2 x 3 x 243
11664 = 2 x 2 x 2 x 2 x 3 x 3 x 81
Let me jump a few steps here
11664 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
Now we make a Trio of similar numbers as,
11644 = (2 x 2 x 2) x (2) x (3 x 3 x 3) x (3 x 3 x 3)
We can see there is only 1 digit left out.
We can multiply it by a pair of same numbers i.e 2 to make the given number a Perfect Cube.
Thus the number if multiplied by 4 becomes a perfect cube (46656 = 36 x 36 x 36).
hope it helps you friend.......