Advertisements
Advertisements
Question
Which is the smallest number that must be multiplied to 77175 to make it a perfect cube?
Advertisements
Solution
The prime factor of 77175 are
| 3 | 77175 |
| 3 | 25725 |
| 5 | 8575 |
| 5 | 1715 |
| 7 | 343 |
| 7 | 49 |
| 7 | 7 |
| 1 |
= 3 x 3 x 5 x 5 x 7 x 7 x 7
= (7 x 7 x 7) x 3 x 3 x 5 x 5
Clearly, 77175 must be multiplied by 3 x 5
= 15
APPEARS IN
RELATED QUESTIONS
Find the cube root of the following number by the prime factorisation method.
110592
Find the cube root of the following number by the prime factorisation method.
175616
You are told that 1331 is a perfect cube. Can you guess without factorization what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768
\[\sqrt[3]{480} = \sqrt[3]{3} \times 2 \times \sqrt[3]{. . .}\]
\[\sqrt[3]{. . .} = \sqrt[3]{4} \times \sqrt[3]{5} \times \sqrt[3]{6}\]
Find The cube root of the numbers 3048625, 20346417, 210644875, 57066625 using the fact that 20346417 = 9261 × 2197 .
Making use of the cube root table, find the cube root
833 .
Find the cube root of 13824 by prime factorisation method.
Using prime factorisation, find which of the following are perfect cubes.
128
Using prime factorisation, find the cube roots of 512
