Use squares, square roots, and reciprocal tables to evaluate 3.0452 + (1)/(sqrt(49.24)).

Morning black — let's get this done. Question 4: Use squares, square roots, and reciprocal tables to evaluate 3.045^2 + (1)/(sqrt(49.24)). Step 1: Evaluate 3.045^2. Using square tables with interpolation or a calculator for precision: 3.045^2 = 9.272025 Rounding to 4 decimal places, as is common with table usage: 3.045^2 ≈ 9.2720 Step 2: Evaluate sqrt(49.24). Using square root tables: Look up sqrt(49.2). This value is approximately 7.014. The mean difference for the fourth digit '4' is 3. So, sqrt(49.24) = 7.014 + 0.003 = 7.017. Step 3: Evaluate (1)/(sqrt(49.24)) = (1)/(7.017). Using reciprocal tables: Look up the reciprocal of 7.01. This value is approximately 0.14265. The mean difference for the fourth digit '7' is 16. For reciprocals, the mean difference is subtracted. So, (1)/(7.017) = 0.14265 - 0.00016 = 0.14249. Rounding to 4 decimal places: (1)/(sqrt(49.24)) ≈ 0.1425 Step 4: Add the two values. 3.045^2 + (1)/(sqrt(49.24)) ≈ 9.2720 + 0.1425 ≈ 9.4145 The evaluated expression is 9.4145. Question 5: Simplify the expression (9x^2 - 25y^2)/(6x^2 - 19xy + 15y^2). Step 1: Factor the numerator. The numerator is a difference of squares, a^2 - b^2 = (a-b)(a+b). Here, a = 3x and b = 5y. 9x^2 - 25y^2 = (3x)^2 - (5y)^2 = (3x - 5y)(3x + 5y) Step 2: Factor the denominator. The denominator is a quadratic expression 6x^2 - 19xy + 15y^2. We look for two binomials (ax+by)(cx+dy). By inspection or trial and error, we find the factors: 6x^2 - 19xy + 15y^2 = (2x - 3y)(3x - 5y) To verify: (2x)(3x) = 6x^2 (2x)(-5y) = -10xy $(-3y)(3x) = -9xy