Question

find the cube root by estimation method
i) 74008
ii) 137592

Answer 1

Step-by-step explanation:

There’s a possibility that you meant to say cube root of 74088, which us exactly 42

But if you really mean 74008, then here’s a trick,

We notice that 42^3 is approx. 74008,

But to be precise, let’s say 74008=42*42*x,

Let’s find that x.

We get x=41.955

Now, let’s find the mean of the factors,

Mean value=(41.955+42+42)/3=41.985

we get the mean factors as 41.985.

Now let’s say 74008=41.985*41.985*y

Let’s find that y.

We get y=41.9846

Now, let’s find the mean of the factors,

Mean value=(41.9846+41.985+41.985)/3=41.9849

we get the mean factors as 41.98487

Now, we can conclude that cube root of 74008 is precisely 41.9849 (although it is still not precise enough as it’s actual, but such manual calculations allow this much percentage error)

Here’s how we can confirm it using calculator

(41.98487)^3=74007.9609

As you can see there is a minute difference of 0.0301 between actual and derived values, which is well acceptable.

Also, cube root of 74008=41.9848774