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By which smallast number must the following number be divided so that the quotient is a perfect cube

(A) 8640


User Katarzyna
by
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2 Answers

5 votes

Hey there! I'm happy to help!

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INTRO TO PERFECT CUBES

A perfect cube is any number whose cube root is an integer. In English, that means that if you take any number without a fraction (this is called an integer, such as -7, 8, 100, none have fractions) and multiply it by itself three times, you get a perfect cube.

If you cube the number 4, you get 64, which is (4×4×4). 64 is an example of a perfect cube.

You can use the cube root button on your calculator to see if a number is a perfect cube. If you do the cube root of 64, you get 4, telling you that 64 is a perfect cube. The cube root of 10 is 2.154434...... so 10 is not a perfect square because it does not give you an integer (number that does not have a fraction) as the answer.

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SOLVING THE PROBLEM

So, we want to find the smallest numbers we can divide 8640 to equal a perfect cube.

I will assume that we will not be dividing by fractions but only whole numbers (positive integers).

We could try dividing by 1, but we see that 8640 is not a perfect cube because it's cube root is 20.519711....

Let's just keep counting up! The first divisor we run into that gives a quotient that it is a perfect cube is the smallest whole number possible that will give us that result.

8640÷2=4320

∛4320≈16.2865....... Not a perfect cube

8640÷3=2880

∛2880≈14.22757..... Not a perfect cube

8640÷4=2160

∛2160≈12.92660..... Not a perfect cube

8640÷5=1728

∛1728=12, a perfect cube!

Since 12 cubed is equal to 1728, this means that 1728 is a perfect square, so 5 is the smallest number we can divide 8640 by to get a perfect square.

The answer is 5.

I hope that this helps! Have a wonderful day! :D

User Jeeeyul
by
7.0k points
1 vote

Answer:

60

Explanation:

8640/60 is 144. 144 is a perfect square. 12*12 is 144

User Xelz
by
7.4k points