Find the cube root of 704/ 1375
Answers
Answer:
he cube root of 1375 can be simplified. So can the cube roots of 1376 and 1377. There are no smaller consecutive three numbers whose cube ...
Step-by-step explanation:
Answer:
Thus, 3 is the required smallest number. (v) Prime factorization of 704 is: 704 = 2 × 2 × 2 × 2 × 2 × 2 × 11 = 23 × 23 × 11 Here, 11 is the smallest number by which 704 is divided to make it a perfect cube, i.e., 704 ÷ 11 = 64 which is a perfect cube.
1375 is a composite number.
Prime factorization: 1375 = 5 × 5 × 5 × 11, which can be written 1375 = 5³ × 11
1375 has at least one exponent greater than 1 in its prime factorization so √1375 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1375 = (√25)(√55) = 5√55
The exponents in the prime factorization are 3 and 1. Adding one to each exponent and multiplying we get (3 + 1)(1 + 1) = 4 × 2 = 8. Therefore 1375 has exactly 8 factors.
The factors of 1375 are outlined with their factor pair partners in the graphic below.
1375 is also the hypotenuse of THREE Pythagorean triples:
385-1320-1375 which is (7-24-25) times 55
484-1287-1375 which is 11 times (44-117-125)
825-1100-1375 which is (3-4-5) times 275