If y^3 = 8.08, approximate y.

Firstly, recognize that 2^3 is 8, so y must be close to 8.It will be helpful to then write y^3 as y^3= 8 + 0.08We can then factorize out 8.y^3=8(1+0.01)If we try and take the cube root of this expression.y=2(1+0.01)^(1/3)
We recognize this is a binomial expansion, if we label x as 0.01 we can see a more familiar form y=2(1+x)^1/3
Expanding this and truncating the expansion for the first order term, we are left with y = 2 + 2x/3
Substituting in, x=0.01 we get y being roughly equal to 2.01

SH
Answered by Sanjith H. Maths tutor

2657 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The rate of decay of the mass is modelled by the differential equation dx/dt = -(5/2)x. Given that x = 60 when t = 0, solve the quation for x in terms of t.


Find exact solution to 2ln(2x+1) - 10 =0


Find, in radians, the general solution of the equation cos(3x) = 0.5giving your answer in terms of pi


Use the substitution u=2+ln(t) to find the exact value of the antiderivative of 1/(t(2+ln(t))^2)dt between e and 1.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning