Question

Find the value of (76)3 by the short cut method​

Answer 1

Answer:

We have to find value of (47)

3

using the short cut method.

We, know that

(a+b)

3

=a

3

+3a

b

+3ab

2

+b

3

So, here we assume a=4 and b=7

Step I

In this step we calculate b

3

∴b

3

=7

3

=34

3

So, unit place of this value is last digit of our answer i.e 3

So, Answer:..3

And, remaining part i.e 34 is added in next step.

Step II:

In this step we calculate 3ab

2

∴3ab

2

=3×4×7

2

=588

Now, 34 from Step I is added to this value.

∴34+588=62

2

So, unit place of this value is 2

nd

last digit of our answer i.e 2

So, Answer:23

And, remaining part i.e 62 is added in next step.

Step III:

In this step we calculate 3a

2

b

∴3a

2

b=3×4

2

×7=336

Now, 62 from Step II is added to this value.

∴62+336=39

8

So, unit place of this value is 3

rd

last digit of our answer i.e 8

So, Answer:....823

And, remaining part i.e 39 is added in next step.

Step IV:

In this step we calculate a

3

∴a

3

=4

3

=64

Now, 39 from Step III is added to this value.

∴39+64=

103

As, this is last step, this whole value is written in front of previous answer to get complete value of cube.

∴ answer:103823

∴(47)

3

=103823