U5L9: Sample work (1pt for correct answer and 1pt for showing work=10pts total)
1.Subtract 5√10 - 3√10
2. Rewrite ∛40 as a product of an integer and another irrational cube root
3. Find area of circle with diameter of 10.2 cm (round to tenth and put units)
4. Find circumference of circle with radius of 2.7 cm (round to tenth and put units)
5. Rewrite √45 in as a product of an integer and irrational square root.
1. To subtract the expressions, we must consider the coefficients of the square roots:
5√10 - 3√10 = (5-3)√10 = 2√10
2. To rewrite ∛40 as a product of an integer and another irrational cube root, we need to find a cube number that divides 40. 2³ = 8 divides 40.
∛40 = ∛(8×5) = ∛8 × ∛5 = 2∛5
3. The formula for the area of a circle is A = πr², where r is the radius.
In this case, the diameter is given, so we need to divide it by 2 to find the radius.
Radius = 10.2 cm / 2 = 5.1 cm
A = π × (5.1)^2 = 81.68 cm²
4. The formula for the circumference of a circle is C = 2πr, where r is the radius.
C = 2π × 2.7 cm ≈ 16.97 cm
5. To rewrite √45 as a product of an integer and irrational square root, we need to find a square number that divides 45. 9 is a square number that divides 45.
√45 = √(9×5) = √9 × √5 = 3√5