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What is the cube of 84?

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592704

692704

593704

693704

answer is A.

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Detailed Solution

The given number is 84.
Using shortcut method.
We know that,

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

Let

a = 8

and

b = 4.

Substitute

a = 8

and

b = 4

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

8 + 4 3 = 83 + 3824 + 3842 + 43

Find

b 3 .

b 3 = 4 × 4 × 4 = 64

Take the last digit 4 for the final answer and the remaining number to be added in the next step.
Find

3 a b 2 .

3 a b 2 = 3842 = 384

Add the remaining number in

3 a b 2 .

⇒ 384 + 6 = 390

Take the last digit 0 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 = 3824 = 768

Add the remaining number in

3 a b 2 .

⇒ 768 + 39 = 807

Take the last digit 7 into the answer next place and the remaining value to be added to the next step.
Find

a 3 .

a 3 = 8 × 8 × 8 = 512

Add the remaining number in

a 3 .

⇒ 512 + 80 = 592

∴ 843 = 592704

Thus the cube of 84 is 592704 and so, option (1) is correct.

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