Final answer:
To expand (1 - x) in ascending powers of x up to the term in x³, we use the binomial theorem. The square root of 7 is approximately 2.64575.
Step-by-step explanation:
To expand (1 - x) in ascending powers of x up to the term in x³, we use the binomial theorem. The binomial theorem states that (a + b)^n = C(n,0)a^n(b^0) + C(n,1)a^(n-1)(b^1) + C(n,2)a^(n-2)(b^2) + ... + C(n,n)a^0(b^n). In this case, a = 1, b = -x, and n = 3. Plugging these values into the formula, we get (1 - x)^3 = C(3,0)(1^3)(-x^0) + C(3,1)(1^2)(-x^1) + C(3,2)(1^1)(-x^2) + C(3,3)(1^0)(-x^3) = 1 - 3x + 3x² - x³.
To find the value of the square root of 7 correct to five decimal places, we use a calculator or a computer program. The square root of 7 is approximately 2.64575.
For finding the square root of 7 correct to five decimal places, we use a calculator or computational software, as manual calculation would be extensive and beyond the scope of this response. The square root of 7 is approximately 2.64575 when rounded to five decimal places.