Simplify radical expressions and perform number theory operations involving primes and composites.

Step 1: Simplify the expression by combining the square roots. sqrt(32x^5y^3)sqrt(4x^3y^2) = sqrt((32x^5y^3)/(4x^3y^2)) Step 2: Simplify the terms inside the square root. sqrt((32)/(4) · (x^5)/(x^3) · (y^3)/(y^2)) = sqrt(8x^5-3)y^3-2 = sqrt(8x^2y) Step 3: Simplify the square root. sqrt(8x^2y) = sqrt(4 · 2 · x^2 · y) = sqrt(4) · sqrt(x^2) · sqrt(2y) = 2xsqrt(2y) The simplified expression is: 2xsqrt(2y) 2. Step 1: Identify prime numbers between 0 and 10. Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves. The prime numbers between 0 and 10 are 2, 3, 5, 7. Writing them in ascending order forms number A: A = 2357 Step 2: Identify odd numbers between 0 and 10. Odd numbers are integers not divisible by 2. The odd numbers between 0 and 10 are 1, 3, 5, 7, 9. Writing them in descending order forms number B: B = 97531 Step 3: Calculate A+B. A+B = 2357 + 97531 = 99888 The value of A+B is: 99888 3. Step 1: List the numbers between 18 and 26. The numbers are 19, 20, 21, 22, 23, 24, 25. Step 2: Classify each number as prime or composite. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A composite number is a natural number greater than 1 that is not prime (i.e., it has at least one divisor other than 1 and itself). • 19: Its only divisors are 1 and 19. So, 19 is a prime number. • 20: It is divisible by 1, 2, 4, 5, 10, 20. So, 20 is a composite number. • 21: It is divisible by 1, 3, 7, 21. So, 21 is a composite number. • 22: It is divisible by 1, 2, 11, 22. So, 22 is a composite number. • 23: Its only divisors are 1 and 23. So, 23 is a prime number. • 24: It is divisible by 1, 2, 3, 4, 6, 8, 12, 24. So, 24 is a composite number. • 25: It is divisible by 1, 5, 25. So, 25 is a composite number. The classification is: Prime numbers: 19, 23 Composite numbers: 20, 21, 22, 24, 25 Send me the next one 📸