Final answer:
To simplify the expression √1764 / 214232 * (72) * (22) * (32) * (72), we find the square root of 1764 which is 42. Then we use the prime factorization of 214232 and other multiplications to see the multiples of 42 cancel each other, ultimately simplifying the expression to 1.
Step-by-step explanation:
The question asks to simplify the expression √1764 / 214232 * (72) * (22) * (32) * (72). Let's break it down step by step:
- The square root of 1764 is 42 because 42^2 = 1764.
- Moving on, we handle the multiplication and division parts of the expression. When we put all the numbers together, we notice that 42 is a multiple of 214232, and all the other factors are powers of prime numbers.
- The prime factorization of 214232 would show multiples of 42.
- After simplifying, it turns out that all the factors outside of the square root will cancel out the 214232 due to the multiples of 42 contained within it.
To simplify the expression √1764 / 214232 * (72) * (22) * (32) * (72), we can perform the calculations step by step.
First, let's simplify the square root of 1764. The square root of 1764 is 42 because 42 * 42 = 1764.
Next, we divide 42 by 214232, which gives us a small decimal. Multiplying this decimal by 72, 22, 32, and 72 yields an even smaller decimal.
Therefore, the simplest form of the expression is approximately 0.
As a result, the entire expression simplifies to 1.