To find the smallest number by which 31250 can be divided to find the perfect cube root of the quotient, we need to perform the following steps:
Step 1: Find the cube root of 31250.
The cube root of 31250 is ∛31250 ≈ 31.25.
Step 2: Determine the quotient.
Divide 31250 by the cube root obtained in Step 1:
31250 ÷ 31.25 = 1000.
Step 3: Find the smallest number by which the quotient can be divided to get a perfect cube.
Since the quotient is 1000, the smallest number by which it can be divided to get a perfect cube is 10.
10 x 1000 = 10000.
Now, check the cube root of 10000:
∛10000 = 10.
As we can see, the cube root of the quotient 1000 is 10, and the smallest number by which 31250 can be divided to find this perfect cube root of 10 is 10.
To find the smallest number by which the number 31250 can be divided to get a perfect cube root of the quotient, we need to find the largest power of the cube root that divides 31250.
The prime factorization of 31250 is:
31250 = 2 * 5^5
To get a perfect cube root of the quotient, we need to make the exponents of all the prime factors in the quotient multiples of 3.
The highest power of 2 that can be a part of a perfect cube is 2^3 = 8.
The highest power of 5 that can be a part of a perfect cube is 5^3 = 125.
So, the smallest number by which 31250 can be divided to find a perfect cube root of the quotient is:
Smallest number = 2^3 * 5^3 = 8 * 125 = 1000
Thus, 1000 is the smallest number by which 31250 can be divided to get a perfect cube root of the quotient.
Answers & Comments
To find the smallest number by which 31250 can be divided to find the perfect cube root of the quotient, we need to perform the following steps:
Step 1: Find the cube root of 31250.
The cube root of 31250 is ∛31250 ≈ 31.25.
Step 2: Determine the quotient.
Divide 31250 by the cube root obtained in Step 1:
31250 ÷ 31.25 = 1000.
Step 3: Find the smallest number by which the quotient can be divided to get a perfect cube.
Since the quotient is 1000, the smallest number by which it can be divided to get a perfect cube is 10.
10 x 1000 = 10000.
Now, check the cube root of 10000:
∛10000 = 10.
As we can see, the cube root of the quotient 1000 is 10, and the smallest number by which 31250 can be divided to find this perfect cube root of 10 is 10.
Answer:
To find the smallest number by which the number 31250 can be divided to get a perfect cube root of the quotient, we need to find the largest power of the cube root that divides 31250.
The prime factorization of 31250 is:
31250 = 2 * 5^5
To get a perfect cube root of the quotient, we need to make the exponents of all the prime factors in the quotient multiples of 3.
The highest power of 2 that can be a part of a perfect cube is 2^3 = 8.
The highest power of 5 that can be a part of a perfect cube is 5^3 = 125.
So, the smallest number by which 31250 can be divided to find a perfect cube root of the quotient is:
Smallest number = 2^3 * 5^3 = 8 * 125 = 1000
Thus, 1000 is the smallest number by which 31250 can be divided to get a perfect cube root of the quotient.
Step-by-step explanation: