{"id":2545,"date":"2021-10-04T05:27:08","date_gmt":"2021-10-04T05:27:08","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2545"},"modified":"2022-01-02T07:12:40","modified_gmt":"2022-01-02T07:12:40","slug":"cube-root-of-a-number-by-division-method","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/cube-root-of-a-number-by-division-method\/","title":{"rendered":"CUBE ROOT OF A NUMBER BY DIVISION METHOD"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.6″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
\n” _builder_version=”4.10.8″ _module_preset=”default” header_font=”|700|||||||” header_text_align=”left” header_font_size=”50px” header_line_height=”1.18em” custom_padding=”|0px||4px|false|false” header_font_size_tablet=”” header_font_size_phone=”35px” header_font_size_last_edited=”on|phone” global_colors_info=”{}”]<\/p>\n

CUBE ROOT OF A NUMBER BY DIVISION METHOD<\/strong><\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.11.3″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” header_3_text_color=”#757575″ custom_padding=”15px|15px||4px|false|false” global_colors_info=”{}”]When the number is multiplied by itself three times, it is said to be the cube of that number and the inverse of it is the cube root. For example – \u2018a\u2019 is the cube root of \u2018a3<\/sup>\u2019 and \u2018a3<\/sup>\u2019 is the cube of \u2018a\u2019. In this article, we are going to learn the division method for finding the cube root of a number.<\/p>\n

 <\/p>\n

FINDING CUBE ROOT BY DIVISION METHOD<\/strong><\/h2>\n

STEPS INVOLVED IN FINDING THE CUBE ROOT<\/h3>\n

To understand the process of finding the cube root of a number by the division method, let us take the number 13824 and try to find the cube root of this number.<\/p>\n

 <\/p>\n

STEP 1<\/strong> – Let us take the digits of the number into groups of threes, starting from the right to the left i.e., from the unit place. In our example, the groups are \u2018824\u2019 and \u201813\u2019.<\/p>\n

STEP 2<\/strong> – We need to find the number whose cube is equal to or less than 13 and subtract the cube of that number from the first group from left to right. In our example, that number is 2 because its cube is \u20188\u2019 which is less than 13. We will subtract it from 13, which is our first group from left to right. So, 2 becomes the first quotient.<\/p>\n

 <\/p>\n

STEP 3<\/strong> – After subtraction, we will bring down the next group. So, we will bring down \u2018824\u2019 and the number that will be formed is 5824.<\/p>\n

STEP 4<\/strong> – Now, we have to find the other digit of the quotient. To find the second digit of the quotient, we will use the following expression –<\/p>\n

[(10a + b)\u00d730a + b2<\/sup>] \u00d7 b<\/p>\n

 <\/p>\n

where\u00a0\u00a0\u00a0\u00a0\u00a0 a = first digit of the quotient,<\/p>\n

b = second digit of the quotient<\/p>\n

(10a + b) = the two-digit number formed by joining a and b.<\/p>\n

 <\/p>\n

In our example, the value of a = 2, so the expression = [30\u00d72(10\u00d72 + b) + b2<\/sup>] \u00d7 b.<\/p>\n

We can simplify this expression as [60(20 + b)+ b2<\/sup>] \u00d7 b.<\/p>\n

 <\/p>\n

STEP 5<\/strong> – We will use the trial and error method for determining the value of \u2018b\u2019 and the value of expression must be less than or equal to the number formed in STEP 3. In our example, it must be equal to or less than 5,824. The trial and error method is as follows –<\/p>\n

b = 1, (60 \u00d7 21 + 12<\/sup>) \u00d7 1 = 1261<\/p>\n

b = 2, (60 \u00d7 22 + 22<\/sup>) \u00d7 2 = 2648<\/p>\n

b = 3, (60 \u00d7 23 + 32<\/sup>) \u00d7 3 = 4167<\/p>\n

b = 4, (60 \u00d7 24 + 42<\/sup>) \u00d7 4 = 5824<\/p>\n

We can see that when b = 4, then the value of the expression is equal to 5824.<\/p>\n

Therefore, 24 is the cube root of 13824. It means that when 24 is multiplied three times by itself,\u00a0 the resultant number is 13824.<\/p>\n

 <\/p>\n

In this way, we can find the cube root of the number. We generally apply the prime factorisation method to find the cube root but when the number is large, the division method becomes easy as compared to the prime factorisation method for finding the cube root of the number. The division method can be applied to both the large and the small numbers.[\/et_pb_text][et_pb_text disabled_on=”on|on|on” admin_label=”Sample Questions
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Practice Multiple Choice Questions<\/h1>\n

[\/et_pb_text][et_pb_text disabled_on=”on|on|on” admin_label=”Question 1″ _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” custom_padding=”25px|25px|25px|25px|true|true” border_radii=”on|15px|15px|15px|15px” border_width_all=”2px” border_color_all=”#000000″ border_width_top=”4px” border_color_top=”#E02B20″ disabled=”on” global_colors_info=”{}”]<\/p>\n

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\n

Questions<\/strong><\/p>\n

Q1. When 343 is divided by 7 and 15 is added to the number, we get the cube of which number?<\/span>
\nSol. The prime factors of 343 = 7\u00d77\u00d77<\/span>
\n\u00a0When 343 is divided by 7, we get =<\/span> 7\u00d77\u00d77<\/span>7<\/span>= 49.<\/span>
\n\u00a0When 15 is added to 49, we get =<\/span> 64\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>
\n\u00a0The prime factors of 64 =\u00a0 2\u00d72\u00d72\u00d72\u00d72\u00d72<\/span>
\n\u00a0When we form the triplets of 2, we get = 2<\/span>3<\/span>\u00d72<\/span>3<\/span> = (2\u00d72)<\/span>3<\/span> = 4<\/span>3<\/span>
\n\u00a0On applying the cube root on 4<\/span>3<\/span>, we get 4, which is the cube root of 64.<\/span><\/p>\n<\/div>\n<\/div>\n

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Explore Other Topics<\/h1>\n

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Geometry<\/a><\/div>\n
Trigonometry<\/a><\/div>\n
Operations<\/a><\/div>\n
Numbers<\/a><\/div>\n<\/div>\n

[\/et_pb_text][et_pb_text admin_label=”Related Concepts
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Related Concepts<\/h1>\n

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\n
Cube and Cube roots<\/a><\/div>\n
How to find the Cube root of a number easily?<\/a><\/div>\n
Cube root of 19683<\/a><\/a><\/div>\n<\/div>\n

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Frequently Asked Questions<\/h1>\n

Q1. What is the radical and exponential form of the cube root of 29?<\/p>\n

Ans The radical form of the cube root of 29 is \u221b29 and the exponential form is 29(1\/3).<\/p>\n

 <\/p>\n

Q2. Is there any other method to find the cube root of 2197?<\/p>\n

Ans. Yes, we can find the cube root of 2197 by using the prime factorisation method.<\/p>\n

The prime factors of 2197 are (13\u00d713\u00d713), which can be written as (133<\/sup>). When we apply the cube root on (133<\/sup>), we get 13, which is the cube root of 2197.<\/p>\n

 <\/p>\n

Q3. How to find the cube root of a decimal number by the division method?<\/p>\n

Ans. Suppose, we have the number 21.952 of which we have to find the cube root.<\/p>\n

So, we will write the cube root of 15.625 in this way (\u221b21952)\/(\u221b1000) and then follow the same process as discussed above.[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

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