Question

4. Find the value of using the short-cut method: (25)^3
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Answer 1

Step-by-step explanation:

(25)^3

15,625

this is your answer

Answer 2

Answer:

(25)3=15625

Step-by-step explanation:

We have to find value of (25)^3 using the short cut method.

We, know that 

(a+b)3=a3+3ab+3ab2+b3

So, here we assume a=2 and b=5

Step I:

In this step we calculate b3

∴b3=53=125

So, unit place of this value is last digit of our answer i.e 5

So, Answer:........5

And, remaining part i.e 12 is added in next step.

Step II:

In this step we calculate 3ab2

∴3ab2=3×2×52=150

Now, 12 from Step I is added to this value.

∴12+150=162

So, unit place of this value is 2ndlast digit of our answer

i.e 2

So, Answer:......25

And, remaining part i.e 16 is added in next step.

Step III:

In this step we calculate 3a2b

∴3a2b=3×22×5=60

Now, 16 from Step II is added to this value.

∴16+60=76

So, unit place of this value is 3rdlast digit of our answer i.e 6

So, Answer:....625

And, remaining part i.e 7 is added in next step.

Step IV:

In this step we calculate a3

∴a3=23=8

Now, 7 from Step III is added to this value.

∴7+8=15

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

∴ answer:15625

∴(25)3=15625