Question

find the smallest whole number must be subtracted from 899tomake it a perfect cube​

Answer 1

AnswEr :

Perfect Cube is the Cube of an Integer.

Ex : ( a )³ = a × a × a, where a is Integer.

In order to make it as perfect cube, once should know the cubes till 10

⋆ No. and Cube till 10 :

⠀⠀⠀1 : 1

⠀⠀⠀2 : 8

⠀⠀⠀3 : 27

⠀⠀⠀4 : 64

⠀⠀⠀5 : 125

⠀⠀⠀6 : 216

⠀⠀⠀7 : 343

⠀⠀⠀8 : 512

⠀⠀⠀9 : 729

⠀⠀⠀10 : 1000

• Let's Head to the Question Now :

Perfect Cubes Near the Number 899 are 729 i.e. cube of 9 and 1000 i.e. cube of 10.

Since the least number was supposed to be subtracted from the given number :

• Let the unknown least be x, Now ;

⇒ 899 - x = ( 9 )³

⇒ 899 - x = 729

⇒ 899 - 729 = x

⇒ x = 170

∴ 170 is that smallest whole number.

Answer 2

$\large\tt{Question:-}$

find the smallest whole number must be subtracted from 899 tomake it a perfect cube ???

${\large\bf{\mid{\overline{\underline{Solution:-}}}\mid}}$

First we will understand what is a cube ?

→ A cube number is a number that is the product of three numbers which are the same.

→ In other words, if you multiply a number by itself and then by itself again, the result is a cube number.

Lets take some Example First :--

(1)³ = 1×1×1 = 1

(2)³ = 2×2×2 = 8

(3)³ = 3×3×3 = 27

_____________

_____________

(x)³ = x × x × x

________________________________

Now, we will see that, first ,,upto 899 which number cube we can go ..

9³ = 9 × 9 × 9 = 729

and,

10³ = 10×10×10 = 1000 .

_______________________________

Hence,

729 < 899 < 1000 = 9³ < 899 < 10³

Nearest Number of cube is of 9 to 899.

As 10³ will be larger to 899 . [ and we have to ask what number must be subtracted] .

so,

whole number must be subtracted = 899 - 729 = $\red{\bold{</strong><strong>1</strong><strong>7</strong><strong>0</strong><strong>}}$

____________________________________

$\large\bold\star\underline\mathcal{Verification:-}$

we have given number = 899

if we subtract 170 , we get = 899-170 = 729

and , 729 is = 9×9×9 = 9³ .

$\textsf{So, we can say that, If we subtract 170 From 899 }$

$\textsf{we will get a perfect cube of 9.}$

$\large\underline\textbf{Hope it Helps You.}$