Verified Answer :

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!(:

Answer:

The solution of the equation is 4.55.

Step-by-step 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.

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