Question

Check whether 256 is perfect cube or perfect square?​

Answer 1

Step-by-step explanation:

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Answer..

Solution :

Resolving 256 into prime factors, we have

256 \: \: = \: \: 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2256=2×2×2×2×2×2×2×2

Grouping the factors in triplets of equal factors , we get:

256 \: = \: (2 \times 2 \times 2) \times (2 \times 2 \times 2) \times 2 \times 2256=(2×2×2)×(2×2×2)×2×2

Clearly in grouping, The factors in triplets of equal factors, we are left with two factors

2 \times 22×2

Therefore, 256 is not a perfect cube.

256 is a perfect sq. no. There are total 16 perfect sq. no. till 256. The sq. of numbers which are factors of 16 will be the factors of 256. There are 5 factor of 16(i.e.1,2,4,8,16).so 5 perfect sq. no. are factors of 256 (1,4,16,64,256).

Answer 2

first we have to know that the numbers ending with 2,3,7or8 are not perfect squares. here 256 is ending with the digit 6.so it is a perfect square.

Now let's do it in another way.

step:-1 split the number up and add each digit together

2+5+6=13

step:-2 if the answer is more than one digit,you would add each digit of the answer together again.

1+3=4

so 4 is the digital root of the number 256.

so 4 is not in the list of 2,3,7or8 which are not perfect square.so 256 is the perfect square