Advertisements
Advertisements
प्रश्न
Find the least number by which 1323 must be multiplied so that the product is a perfect cube.
Advertisements
उत्तर
1323 = 3 × 3 × 3 × 7 × 7
= 33 × 72
To make it a perfect cube, the power of each prime factor must be a multiple of 3.
The power of 3 is already 3, but the power of 7 is 2.
We need one more 7 to make it 73.
So, multiply 1323 by 7.
1323 × 7 = 9261
9261 is a perfect cube.
Therefore, the least number is 7.
APPEARS IN
संबंधित प्रश्न
Find the smallest number by which the following number must be divided to obtain a perfect cube.
81
Find the smallest number by which the following number must be divided to obtain a perfect cube.
192
Find the cubes of the number 7 .
Find the cubes of the number 21 .
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 which are multiples of 7 and verify the following:
'The cube of a multiple of 7 is a multiple of 73'.
Which of the following is perfect cube?
456533
By which smallest number must the following number be divided so that the quotient is a perfect cube?
107811
Find if the following number is not a perfect cube?
243
By taking three different values of n verify the truth of the following statement:
If n is even , then n3 is also even.
Write true (T) or false (F) for the following statement:
If a2 ends in an even number of zeros, then a3 ends in an odd number of zeros.
Find the smallest number that must be subtracted from those of the numbers in question 2 which are not perfect cubes, to make them perfect cubes. What are the corresponding cube roots?
Find the cube root of the following natural number 1157625 .
Find the cube root of the following integer −125 .
Show that:\[\sqrt[3]{- 125 - 1000} = \sqrt[3]{- 125} \times \sqrt[3]{- 1000}\]
Making use of the cube root table, find the cube root
1346.
Find the cube-root of -2744000
The smallest number to be added to 3333 to make it a perfect cube is ___________
The cube of 0.0012 is 0.000001728.
Find two smallest perfect square numbers which when multiplied together gives a perfect cube number
