10. Estimate the square root and cube root of the following upto one decimal place:
(iii) 850
Answers
Given : Number 850
To find : estimate the square root and cube root up to one decimal places
Solution:
f(x) = √x
f(850) = √850
f(x + Δx) = √(900 - 50)
x = 900 Δx = - 50
f'(x) = 1/2√x
f(x + Δx) = f(x) + f'(x) Δx
=> √850 = √900 + (1/2√900)(-50)
=> √850 = 30 - 50/60
=> √850 = 30 - 0.833
=> √850 = 29.167
=> √850 = 29.2
f(x) = ∛x
f(850) = ∛850
f(x + Δx) = ∛(1000 - 150 )
x = 1000 Δx = -150
f'(x) = (1/3 (∛x )²
f(x + Δx) = f(x) + f'(x) Δx
=> ∛850 = ∛100 + (1/3(∛(1000)²)(-150)
=> ∛850 = 10 -150/300
=> ∛850 = 10 - 0.5
=> ∛850 = 9.5
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