Find the Product of sqrt(3) and 2sqrt(5) 2. Write the expansion of 2x(sqrt(3) - 4sqrt(2)) 3. find the Sun of (3sqrt(5)-4sqrt(2)) and (3sqrt(5)+5sqrt(2)) 4. Simplify sqrt(240)

Here are the solutions to your homework problems: 1. Find the Product of 4sqrt(3) and 2sqrt(5) Step 1: Multiply the coefficients and the terms under the square root. (4sqrt(3)) × (2sqrt(5)) = (4 × 2) × (sqrt(3) × sqrt(5)) Step 2: Simplify the product. 8 × sqrt(3 × 5) = 8sqrt(15) The product is 8sqrt(15). 2. Write the expansion of 2x(4sqrt(3) - sqrt(2)) Step 1: Distribute 2x to each term inside the parenthesis. 2x(4sqrt(3) - sqrt(2)) = (2x × 4sqrt(3)) - (2x × sqrt(2)) Step 2: Simplify each product. 8xsqrt(3) - 2xsqrt(2) The expansion is 8xsqrt(3) - 2xsqrt(2). 3. Find the Sum of (3sqrt(5) - 4sqrt(2)) and (3sqrt(5) + 5sqrt(2)) Step 1: Combine the two expressions by addition. (3sqrt(5) - 4sqrt(2)) + (3sqrt(5) + 5sqrt(2)) Step 2: Group like terms (terms with sqrt(5) and terms with sqrt(2)). (3sqrt(5) + 3sqrt(5)) + (-4sqrt(2) + 5sqrt(2)) Step 3: Add the coefficients of the like terms. (3+3)sqrt(5) + (-4+5)sqrt(2) = 6sqrt(5) + 1sqrt(2) The sum is 6sqrt(5) + sqrt(2). 4. Simplify sqrt(240) Step 1: Find the largest perfect square factor of 240. The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240. The perfect square factors are 1, 4, 16. The largest is 16. So, 240 = 16 × 15. Step 2: Rewrite the square root using the factors. sqrt(240) = sqrt(16 × 15) Step 3: Simplify the perfect square factor. sqrt(16) × sqrt(15) = 4sqrt(15) The simplified form is 4sqrt(15). Send me the next one 📸