Question

find the ones digit of the cube of 1453​

Answer 1

Answer:

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Step-by-step explanation:

The cubed root of one thousand, four hundred and fifty-three ∛1453 = 11.326312452767

Answer 2

Answer:

Find the one’s digit of the cube of each of the following numbers.

i) 3332

ii) 8888

iii) 1492

iv) 1005

v) 1024

vi) 77

vii) 5022

viii) 53

Answer

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Hint: Here we are given a few numbers, and we have to find the last digit of the cube of that particular number. Here the last digit is the same as the one’s digit of any number. Here finding the last digit or one’s digit of the cube of a given number, is the same as cubing the last digit of that particular number, and the cube of the last digit of that number is the one’s digit of the cube.

Cube of a number a, is given by the exponent of 3, while the base is a.

⇒a3=A

Complete step-by-step solution:

Given the numbers and after finding the cube of the number we have to find the one’s digit of that cubed number.

i. First considering the number 3332

Here the last digit of 3332 is 2.

The cube of 2 is 8.

⇒23=8

Here the last digit of 23 is 8.

Hence the one’s digit of the cube of 3332 is 8.

ii. Now consider the second number 8888

Here the last digit of 8888 is 8.

The cube of 8 is 512.

⇒83=512

Here the last digit of 83 is 2.

Hence the one’s digit of the cube of 8888 is 2.

iii. Now consider the next number 1492

Here the last digit of 1492 is 2.

The cube of 2 is 8.

⇒23=8

Here the last digit of 23 is 8.

Hence the one’s digit of the cube of 1492 is 8.

iv. Now consider the next number 1005

Here the last digit of 1005 is 5.

The cube of 5 is 125.

⇒53=125

Here the last digit of 53 is 5.

Hence the one’s digit of the cube of 1005 is 5.

v. Now consider the next number 1024

Here the last digit of 1024 is 4.

The cube of 4 is 64.

⇒43=64

Here the last digit of 43 is 4.

Hence the one’s digit of the cube of 1024 is 4.

vi. Now consider the next number 77

Here the last digit of 77 is 7.

The cube of 7 is 343.

⇒73=343

Here the last digit of 73 is 3.

Hence the one’s digit of the cube of 77 is 3.

vii. Now consider the next number 5022

Here the last digit of 5022 is 2.

The cube of 2 is 8.

⇒23=8

Here the last digit of 23 is 8.

Hence the one’s digit of the cube of 5022 is 8.

viii. Now consider the next number 53

Here the last digit of 53 is 3.

The cube of 3 is 27.

⇒33=27

Here the last digit of 33 is 7.

Hence the one’s digit of the cube of 53 is 7.

Note: While solving this be careful and do not get confused in choosing the right digit of the number. Here in order to find the last digit of the cube of a number, instead of a big process of multiplying the number with itself for 3 times results in a tedious process. Hence we are just finding the cube of the last digit of the given number, and the resulting last digit of the last digit cube is the one’s digit of the cube of the given number.

Step-by-step explanation:

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