Question

3√110592 (cube root of 110592) BY ESTIMATION METHOD.
ONE WITH THE BEST ANSWER WILL SURELY BE CHOSEN AS THE BRAINLIEST ANSWER. please answer ONLY IN ESTIMATION METHOD.
PLEASE
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Answer 1

Solution :

Cube root of a number through estimation.

Given number = 110592

Step 1 : Start making the groups of three digits starting from the right most digit of the number, i.e.

• Second Group - 110

• First Group - 592

Step 2 : From the first group 592,take the digit from ones place. This is 2,which will be the ones digit in the cube root of the given number (as 2³ = 8 so 8 in the ones place of the required cube root).

Step 3 : Now, take other group i.e. 110

We know that 64 < 110 < 125

i.e. 4³ < 110 < 5³

So we take the ones place of the smaller number, i.e. 4 as the tens place of the required cube root.

$\therefore\sf \: \sqrt[3]{110592} \: = 48$

Answer 2

$\sf{\underline{\red{The\: cube \:root \:of \:110592\: is<strong> </strong>\:48}}}$

• It is known that the cube root of six digit number has two digits,units and tens place digit.

Let the ten's place digit be x.

Let the unit's place digit be y.

Cube root : 10x + y

•Split the given number consecutively into two groups of three digit number.

First group : 110

Second group : 592

•Since 592 is the last group of digit ending with 2 which indicates that 110592 is a perfect cube whose cube root number ends with 8.

Why?

•For a number to be a perfect cube, the cube root of the number must end with 1,8,7,4,5,6,3,2,9 and 0.

That's the rule, can't play here.

We have the units digit of our cube root that is,8 (y).

•Now consider the first group of digits, 110.

•We know that 110 is a number which would lie between the cubes of 4 and 5.

Cube of 4 = 64

Cube of 5 = 125

•Hence it's clear that 110 lies between the cube of 4 and 5,which are of course perfect cubes.

So we can say that 11052 lies between 40³ and 50³.

We already have the unit's digit of our cube root,8.

Now,there is just one possibility of a number having 8 as the unit's place and that is 48.

•The ten's place,x of the cube root number is 4 and unit's place,y is 8.

$\bold{Cube\: root\: =\: 10(4) \:+\: 8 \:= \:40 \:+\: 8 \:= 48.}$