By what number 231525 to make it perfect cube. Find the cube root of the number after multiplying
Answers
Answer:
Step-by-step explanation:
231525=3³×5²×7³
Multiplying both sides by 5
231525×5=3³×5³×7³ Which is a perfect cube no.
hence 231525 is to be multiplied by 5 to make it perfect cube no.
Now ∛3³×5²×7³
= 3×5×7
= 105
Given,
The number 231525 is given.
To find,
We have to find the number by which 231525 must be multiplied so that it becomes a perfect cube and we have to find the cube root of the number so obtained after multiplying.
Solution,
The number 231525 must be multiplied by 5 to make it a perfect cube and the cube root of the number after multiplying is 105.
The prime factorization of 231525 is 3³ * 5² * 7³.
To make the number 231525 a perfect square, we have to multiply it by 5.
231525 * 5 = 3³ * 5³ * 7³
For cube root, taking the cube root on RHS, we get
= ∛3³ * ∛5³ * ∛7³
= 3 * 5 * 7
= 105
So, the cube root of the number formed after multiplying is 105.
Hence, the number 231525 must be multiplied by 5 to make it a perfect cube and the cube root of the number after multiplying is 105.