Express 5832 as a product of prime factors and hence,find the cube root of 5832 ?
Use you divisibility rules: You know it is divisible by 2 (even last number) and 3 (sum of digits is divisible by 3). Start there.
I will give you the cube root and you can do the rest.
The cube root is a number that when multiplied 3 times by itself will yield 5832, in this case.
The cube root is 18.
Why 18?
Because 18 x 18 x 18 = 5832.
You finish the question.
To express 5832 as a product of prime factors, we need to factorize it into its prime factors.
Step 1: Start with the smallest prime number, which is 2.
5832 ÷ 2 = 2916 => 2^1 * 2916
Step 2: Divide the quotient by 2 until it is no longer divisible by 2.
2916 ÷ 2 = 1458 => 2^2 * 1458
1458 ÷ 2 = 729 => 2^3 * 729
Step 3: Now, move on to the next prime number, which is 3.
729 ÷ 3 = 243 => 2^3 * 3^5
Step 4: Continuing with the same process, divide the quotient by 3 until it is no longer divisible by 3.
243 ÷ 3 = 81 => 2^3 * 3^4
81 ÷ 3 = 27 => 2^3 * 3^3
Step 5: Next, divide the quotient by 3 until it is no longer divisible by 3.
27 ÷ 3 = 9 => 2^3 * 3^2
9 ÷ 3 = 3 => 2^3 * 3^1
Now, we have 5832 expressed as the product of prime factors: 2^3 * 3^1.
To find the cube root of 5832, we need to find the cube root of each factor and then multiply them.
The cube root of 2^3 is 2.
The cube root of 3^1 is 3.
Therefore, the cube root of 5832 is 2 * 3 = 6.
So, the prime factorization of 5832 is 2^3 * 3^1, and the cube root of 5832 is 6.