Question

2 Misha wrote a 3-digit number such that its last two digits form the cube of 4 and the left most digit is the cube root of a number which is 2 less than the sum of the last two digits. What number does Misha wrote?​

Answer 1

Given that:

• Misha wrote a 3-digit number such that its last two digits form the cube of 4.
• The left most digit is the cube root of a number which is 2 less than the sum of the last two digits.

To Find:

• What number does Misha wrote?

Finding the last two digits:

• Cube of 4 = 4³
• Cube of 4 = 4 × 4 × 4
• Cube of 4 = 64

Find the left most digit:

Adding the last two digits.

• 6 + 4 = 10

Subtracting 2 from the sum.

• 10 - 2 = 8

Finding cube root.

• Cube root of 8 = 2

Now we have:

• Hundreds digit = 2
• Tens digit = 6
• Ones digit = 4

∴ The required number = 264

Hence,

• The number written by Misha is 264.

Answer 2

Given that , Misha wrote a 3-digit number such that its last two digits form the cube of 4 and the left most digit is the cube root of a number which is 2 less than the sum of the last two digits.

Exigency To Find : The three - digit Number written by Misha ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀¤ Finding The three - digit number written by Misha :

⠀⠀⠀⠀⠀⊙ The Last two -- Digit Number :

Given that ,

• It's last two digits form the cube of 4 .

$\qquad \therefore \sf Last_{(\:Two\:-\:Digit \:Number \:)} = \:4^3$

$\qquad \dashrightarrow \sf Last_{(\:Two\:-\:Digit \:Number \:)} = \:4^3$

$\qquad \dashrightarrow \sf Last_{(\:Two\:-\:Digit \:Number \:)} = \:4^3 = 4 \times 4 \times 4$

$\qquad \dashrightarrow \sf Last_{(\:Two\:-\:Digit \:Number \:)} = \:4^3 = 64$

$\dashrightarrow \underline {\boxed {\pmb{\pink{ \frak { \: Last_{(\:Two\:-\:Digit \:Number \:)} = 64\:\:}}}}}\:\:\bigstar$

• Last two- digit number is 64 .

And ,

⠀⠀⠀⠀⠀⊙ The Left most Digit :

• The left most digit is the cube root of a number which is 2 less than the sum of the last two digits.

$\qquad \therefore \sf Left\:Most\:_{ ( Digit )} \:= \: \sqrt[3]{Sum\:_{(\: Last \:two \:digit \:number \:)} - 2 }\:$

$\qquad \dashrightarrow \sf Left\:Most\:_{ ( Digit )} \:= \: \sqrt[3]{Sum\:_{(\: Last \:two \:digit \:number \:)} - 2 }\:$

$\qquad \dashrightarrow \sf Left\:Most\:_{ ( Digit )} \:= \: \sqrt[3]{ ( 6 + 4 ) - 2 }\:$

$\qquad \dashrightarrow \sf Left\:Most\:_{ ( Digit )} \:= \: \sqrt[3]{ 10 - 2 }\:$

$\qquad \dashrightarrow \sf Left\:Most\:_{ ( Digit )} \:= \: \sqrt[3]{ 8 }\:$

$\qquad \dashrightarrow \sf Left\:Most\:_{ ( Digit )} \:= \: 2\:$

$\dashrightarrow \underline {\boxed {\pmb{\pink{ \frak { \:Left\:Most\:_{ ( Digit )} \:= \: 2 \:\:}}}}}\:\:\bigstar$

• The Left most Digit is 2 .

We get ,

• Digit at Hundred's place : 2
• Digit at ten's place : 6
• Digit at one's place : 4

Therefore,

• The number is 264 .

$\qquad \therefore \underline {\sf Hence, \:The \:three \:-\:Digit \:number \:is \:\pmb{\bf 264 \:}\:.}$