Cube Roots 2

Mental calculations:

$\sqrt[3]{125} = 5$ , that's definition.

Now for $\sqrt[3]{941192}$ , we can see it is a $6$ -digit number, so the answer must be a $2$ -digit number. $941192$ ends in $2$ and because of $8^{3}$ ends with 2, the last digit must be $\boxed{8}$ . Now consider the first three digits: $941$ , we can totally see that it's larger than $9^{3}$ but smaller than $10^{3}$ , so the first digit must be $\boxed{9}$ . Therefore, $\sqrt[3]{941192} =98$

For $\sqrt[3]{157464}$ , the answer is a $2$ -digit number, $157464$ end in 4 so the last digit is $\boxed{4}$ . $157$ is larger than $5^{3}$ but smaller than $6^{3}$ so the first digit must be $\boxed{5}$ . Therefore, $\sqrt[3]{157464} = 54$

Now we just need to calculate: $5 \times (98 - 54) = 220$

simplifying we get 5(98-48)=220 take cube root!!

Your note is good

By following the note, let's see that for 941192 , Here the last three digit's (192) last digit is 2 but the cube of 2's last digit is not 2 but the last of the cube of 8 is 2.

So the last digit of the cube root of 941192 is 8.

Next, 941 is nearer and bigger than the cube of 9 , that is 729, So the desired cube root of 941192 is 98.

Similarly, the cube root of 157464 is 58, then simplifying , we get

5 X ( 98 - 58 ) == 220