Advertisements
Advertisements
प्रश्न
By which smallest number must the following number be divided so that the quotient is a perfect cube?
35721
Advertisements
उत्तर
On factorising 35721 into prime factors, we get:
\[35721 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 7 \times 7\]
On grouping the factors in triples of equal factors, we get:
\[35721 = \left\{ 3 \times 3 \times 3 \right\} \times \left\{ 3 \times 3 \times 3 \right\} \times 7 \times 7\]
It is evident that the prime factors of 35721 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 35721 is a not perfect cube. However, if the number is divided by (\[7 \times 7 = 49\]), the factors can be grouped into triples of equal factors such that no factor is left over.
Thus, 35721 should be divided by 49 to make it a perfect cube.
APPEARS IN
संबंधित प्रश्न
Write the cubes of all natural numbers between 1 and 10 and verify the following statements:
(i) Cubes of all odd natural numbers are odd.
(ii) Cubes of all even natural numbers are even.
Write the cubes of 5 natural numbers of the form 3n + 2 (i.e. 5, 8, 11, ...) and verify the following:
'The cube of a natural number of the form 3n + 2 is a natural number of the same form i.e. when it is dividend by 3 the remainder is 2'.
Which of the following is perfect cube?
3087
For of the non-perfect cubes in Q. No. 20 find the smallest number by which it must be multiplied so that the product is a perfect cube.
Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 98784. Find the numbers.
Show that:
\[\frac{\sqrt[3]{729}}{\sqrt[3]{1000}} = \sqrt[3]{\frac{729}{1000}}\]
Find the least number by which 1323 must be multiplied so that the product is a perfect cube.
Find the smallest number by which 10985 should be divided so that the quotient is a perfect cube
Square root of a number x is denoted by `sqrt(x)`.
Three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 0.334125. Find the numbers.
