Question

last two digit of a number 2857 to the power 179​

Answer 1

Answer:

Here is ur answer

Find the last two digits of

2234

31123

7335

There are two-three shortcut approaches to solve the above problems. But before we go and apply the same, we need to understand the following basic points.

Finding the last two digits of a square of any number:

Let’s take an example; say we need to find the last two digits of 782. The prerequisite is to memorise the square of the first 25 natural numbers.

Now, number 78 is close to 100 and the deviation of 78 from 100 is 22 (100-78). So we can write 782=(100–22)2=1002–2×100×22+222=10000–4400+484

Now observe that the last two digits of the first two terms are 00, 00, and 84.

So the last two digits of 782≡ last two digits of (100–22)2≡ last two digits of 222 Similarly, the last two digits of 612≡(50+11)2≡112≡21

From the above examples, we can deduce that the if the number is close to 100 or 50, the last two digits of the square of the number is equal to the last two digits of the square of the deviation of the number from the base 100 or 50 (whichever the number if close to).

Finding the tens place digit of any number with unit digit equal to 1

Say we need to find the last two digits of 3176.

The trick to finding the second last digit of any number ending with 1 is the UNIT DIGIT of the product of the unit digit of the power and the ten’s digit of the base.

It is clear that the unit digit of the given number is 1 and we have to identify the ten’s place digit of the same.

In 3176, the base is 31 (ten’s place is 3) and power is 76 (the unit digit is 6) . So the second last (ten’s digit) of 3176 is Unit digit of 3×6=18 or 8.

Therefore, the last two digits of 3176 are 81.

Note: To verify the above result, we can use the concept of binomial expansion. I leave the same to the readers to do.

Answer 2

Answer:

So,

$57 {}^{179 }$

Step-by-step explanation:

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