Cube using Column Method


 
 
Concept Explanation
 

Cube using Column Method

Let x = ab (where a is the tens digit and b is the units digit ) be a two-digit natural number.

Recall that for finding x^{2}=(ab)^{2},we formed three columns containing a^2, dpi{100} 2times a;times ;b;and ; {b^{2}}, because ({a+b})^{2}=a^{2}+2ab+b^{2}

Since ({a+b})^{3}= {a}^{3} +3a^{2}{b} + 3^{ab^{2}} +^{b^{3}}.

Therefore, for finding x^{3}=(ab)^{3} we will form four columns containing a^{3}, 3times ;^{a^{2}} times b,3 times a times ^{b^{2}} and b^{3} .

The remaining procedure is exactly identical to the method of finding the square of a two-digit natural number.

Illustration: Find the cube of 24 by using the column method .

Solution: Here, a = 2 and b = 4 .

Column I

a^{3}

Column II

3times ^{a^{2}} times b

Column III

3 times a times ^{b^{2}}

Column IV

b^{3}

 2^{3}=8

      +5

3 times ^{2^{2}} times 4 = 48

                 +10

3 times 2 times ^{4^{2}} =96

                 +6

4^{3}=64

 

      13                    58                  102  

       13                                8                                   2                               4

therefore  (24)^{3}=13824

Illustration: Find the cube of 25 by using the column method.

Solution: Here, a = 2 and b = 5 .

Column I

a^{3}

Column II

3times ^{a^{2}} times b

Column III

3 times a times ^{b^{2}}

Column IV

b^{3}

2^{3}=8

         +7

3 times 2^{2} times 5=60

                          +16

3 times 2 times 5^{2}=150

                             +12

5^{3}=125
      15                                76                              162  

15                                           6                                             2                           5

therefore (25)^{3}=15625

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Sample Questions
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Question : 1

Find the number obtained in the third column while calculating the cube of 34 using the column method.

Right Option : A
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Explanation
Question : 2

Find the number obtained in the second column while calculating the cube of 99 using the column method.

Right Option : C
View Explanation
Explanation
Question : 3

Find the number obtained in the second column while finding the cube of 125 using the column method.

Right Option : B
View Explanation
Explanation
 
 


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