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What would be the cube of 68?

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314432

314456

316762

317652

answer is A.

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Detailed Solution

The given number is 68.
We know that,

a + b 3 = a 3 + 3 a 2 b + 3 a b 2 + b 3

Let’s take

a = 6

and

b = 8.

Substitute

a = 6

and

b = 8

a + b 3 = a 3 + 3 a 2 b + 3 a b 2 + b 3 .

⇒ 6 + 8 3 = 63 + 3628 + 3682 + 83

Find

b 3 .

b 3 = 8 × 8 × 8 = 512

Take the last digit 2 for the final answer and the remaining number to be added in the next step.
Find

3 a b 2 .

3 a b 2 = 3682 = 1152

Add the remaining number in

⇒ 1152 + 51 = 1203

Take the last digit 3 into the answer next place and the remaining value to be added to the next step.
Find

3 a 2 b .

3 a 2 b = 3628 = 864

Add the remaining number in

3 a b 2 .

⇒ 864 + 120 = 984

Take the last digit 4 into the answer next place and the remaining value to be added to the next step.
Find

a 3 .

a 3 = 6 × 6 × 6 = 216

Add the remaining number in

a 3 .

⇒ 216 + 98 = 314

∴ 683 = 314432

Thus, the cube of 68 is 314432.
Hence, option (1) is correct.

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What would be the cube of 68?

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