Question

Whats is good estimate for the solution to the equation x³=95? how did you come up with ur estimate

Answer 1

The solution of the equation is 4.55.

Explanation:

Given : Equation
`x^3=95`

To find : Whats is good estimate for the solution to the equation? How did you come up with your estimate ?

Solution :

Equation
`x^3=95`

Taking cube both side,

`x=\sqrt[3]{95}`

As 95 is not a perfect cube so we have to find two consecutive perfect cube that 95 is between.

i.e.
`4^3=64\ , \ 5^3=125`

So,
`\sqrt[3]{64}<\sqrt[3]{95}< \sqrt[3]{125}`

or
`4<\sqrt[3]{95}<5`

Cube root of 95 lies between 4 and 5.

To find a better estimate, first choose number between 4 and 5 and cube them.

`4.5^3=91.125\\4.55^3=94.20\\4.6^3=97.336`

A good estimate for
`\sqrt[3]{95}=4.55`

Therefore, The solution of the equation is 4.55.

Answer 2

Let x =4, so when you plug it in, you get: 4^3 = 64
and
Let x =5, so when you plug it in, you get 5^3=125

95 is in between 64 and 125, so an estimate of what x could be if x^3=95 would be around 4.5.
Hope this helped!(: