The smallest number is 150, which when multiply by 4860; becomes a perfect cube.
Step-by-step explanation:
Given:
To find:
- Find the smallest number by which 4860 should be multiplied so that the product is a perfect cube.
Solution:
Concept to be used:
- Prime factorise the number.
- Make pairs of 3-3 same prime numbers; because [tex]\bf \sqrt[3]{ {a}^{3} } = a[/tex]
Step 1:
Write prime factors of 4860.
[tex]4860 = 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 5 \\ [/tex]
or
[tex]4860 =( 2 \times 2) \times (3 \times 3 \times 3) \times (3 \times 3 )\times (5 )\\ [/tex].
Step 2:
Complete the triplets.
In first bracket; multiply 2,to complete the triplet.
Second triplet is complete.
In third bracket, multiply 3, to complete the triplet.
In fourth bracket, multiply 25, to complete the triplet.
So,
[tex]2 \times 3 \times 25 = 150 \\ [/tex]
If we multiply 150 to 4860, it will become 729000; which is a perfect cube of 90.
Thus,
The smallest number is 150, which when multiply by 4860; becomes a perfect cube.
Learn more:
1) find the smallest number by 13720 must be multiplied to obtain a perfect cube
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2) The smallest number by which 1944 should be multiplied so that it becomes a
perfect cube is-
(i)3
(ii) 2
(iii)5
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