Apply the square root property sqrt((a)/(b)) = sqrt(a)sqrt(b).

Here are the solutions to the problems: Problem 1: Simplify sqrt((32)/(81)) Step 1: Apply the square root property sqrt((a)/(b)) = sqrt(a)sqrt(b). sqrt((32)/(81)) = sqrt(32)sqrt(81) Step 2: Simplify the square roots in the numerator and denominator. We know that sqrt(81) = 9. For sqrt(32), find the largest perfect square factor of 32. 32 = 16 × 2. sqrt(32) = sqrt(16 × 2) = sqrt(16) × sqrt(2) = 4sqrt(2) Step 3: Substitute the simplified square roots back into the fraction. 4sqrt(2)9 The simplified expression is: 4sqrt(2)9 Problem 2: Evaluate sqrt((32)/(128)) - (1)/(3) Step 1: Simplify the fraction inside the square root. (32)/(128) = (32 ÷ 32)/(128 ÷ 32) = (1)/(4) Step 2: Calculate the square root of the simplified fraction. sqrt((1)/(4)) = sqrt(1)sqrt(4) = (1)/(2) Step 3: Perform the subtraction. (1)/(2) - (1)/(3) To subtract, find a common denominator, which is 6. (1 × 3)/(2 × 3) - (1 × 2)/(3 × 2) = (3)/(6) - (2)/(6) Step 4: Subtract the numerators. (3 - 2)/(6) = (1)/(6) The result is: (1)/(6) Problem 3: Evaluate 0.13 × 0.05 Step 1: Multiply the numbers as if they were whole numbers. 13 × 5 = 65 Step 2: Count the total number of decimal places in the original numbers. 0.13 has 2 decimal places. 0.05 has 2 decimal places. Total decimal places = 2 + 2 = 4. Step 3: Place the decimal point in the product so that it has 4 decimal places. Starting with 65, move the decimal point 4 places to the left, adding leading zeros as needed. 0.0065 The product is: 0.0065 Send me the next one 📸