{"id":2553,"date":"2021-10-04T05:43:29","date_gmt":"2021-10-04T05:43:29","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2553"},"modified":"2022-01-02T07:12:08","modified_gmt":"2022-01-02T07:12:08","slug":"cube-of-12-value-and-methods-to-find-it","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/cube-of-12-value-and-methods-to-find-it\/","title":{"rendered":"Cube of 12- Value and methods to find it"},"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 of 12- Value and methods to find it<\/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=”gcid-c32b01a8-824d-42b7-9316-c38ff0e74055″ custom_padding=”15px|15px||4px|false|false” global_colors_info=”{%22gcid-c32b01a8-824d-42b7-9316-c38ff0e74055%22:%91%22header_3_text_color%22%93}”]<\/p>\n

Multiplying a number three times by itself yields a number which is the cube of the original number. The exponential form of a cube is x3<\/sup>. So, In this article, we will discuss the value of the cube of 12 and the methods to find the cube.<\/p>\n

 <\/p>\n

Cube of 12<\/strong><\/h2>\n

The value of the cube of 12 is 1728. We will find the cube of 12 by using the multiplication method and algebraic expressions.<\/p>\n

Method 1 – Multiplication method<\/strong><\/h3>\n

In this method, we need to multiply the number three times by itself to get the cube of that number. It is the simplest method to find the cube of any small number.<\/p>\n

The cube of 12 = 123<\/sup><\/p>\n

= 12\u00d712\u00d712<\/p>\n

= 1728<\/p>\n

 <\/p>\n

Method 2 – Algebraic expression<\/strong><\/h3>\n

In this method, we can use either of the two algebraic expressions to find the cube. We will get the same answer from both expressions. The expressions are –<\/p>\n

Expression 1- (p + q)3<\/sup> = p3<\/sup> + q3<\/sup> + 3pq(p + q)<\/p>\n

Expression 2- (p – q)3<\/sup> = p3<\/sup> – q3<\/sup> – 3pq(p – q)<\/p>\n

We will find the cube of 12 by using both the expressions –<\/p>\n

First, let us write 12 as (10 + 2) for using the first expression, where p = 10, q = 2<\/p>\n

(10 + 2)3<\/sup> = 103<\/sup> + 23<\/sup> + 3\u00d710\u00d72(10 + 2)<\/p>\n

= 1000 + 8 + 60\u00d712<\/p>\n

= 1728<\/p>\n

 <\/p>\n

Now, we will use the second expression. For that, we will write 12 as (15 – 3), where p=15, q=3.<\/p>\n

(15 – 3)3<\/sup> = 153<\/sup> – 33<\/sup> – 3153(15 – 3)<\/p>\n

= 3375 – 27 – 135\u00d712<\/p>\n

= 3375 – 1647<\/p>\n

= 1728<\/p>\n

 <\/p>\n

Illustration<\/strong><\/h2>\n

Q1. Find the value of a and b when a3<\/sup> \u00d7 b3<\/sup> = 123<\/sup>.<\/p>\n

Sol. We know that the value of the cube of 12 = 1728<\/p>\n

To find the value of a and b, we need to do the prime factorisation of 1728.<\/p>\n

The prime factorisation of 1728 = 2\u00d72\u00d72\u00d72\u00d72\u00d72\u00d73\u00d73\u00d73<\/p>\n

We will make the pair of threes – 23<\/sup>\u00d723<\/sup>\u00d733<\/sup><\/p>\n

You can see that we have to find the value of a and b, but we are getting three pairs.<\/p>\n

We will use the identity – xm<\/sup>\u00d7ym<\/sup> = (xy)m<\/sup>.<\/p>\n

 <\/p>\n

Using the above formula we can write 1728 = (2\u00d72)3<\/sup> \u00d7 33<\/sup>.<\/p>\n

The value of a3<\/sup> \u00d7 b3<\/sup> = 43<\/sup>\u00d733<\/sup>,<\/p>\n

if a=4, then b=3<\/p>\n

Or\u00a0\u00a0\u00a0 if a=3, then b=4.<\/p>\n

 <\/p>\n

We can also write 1728 = (2\u00d73)3<\/sup> \u00d7 23<\/sup>= 63<\/sup>\u00d723<\/sup>.<\/p>\n

Here, a3<\/sup> \u00d7 b3<\/sup> = 63<\/sup>\u00d723<\/sup>, if a=6, then b=2 or if a=2, then b=6.<\/p>\n

 <\/p>\n

Q2. When the cube of 12 is divided by the cube of 6, we get the cube of which number?<\/p>\n

Ans. The values of the cube of 6 and 12 are 216 and 1728 respectively.<\/p>\n

When 1728 is divided by 216 = 8.<\/p>\n

The prime factors of 8 are 2\u00d72\u00d72 = 23<\/sup>.<\/p>\n

On applying the cube root on 23<\/sup>, we get 2 as the cube root of 8.<\/p>\n

Therefore, when the cube of 12 is divided by the cube of 6, we get the cube of 2.<\/p>\n

[\/et_pb_text][et_pb_text disabled_on=”on|on|on” admin_label=”Sample Questions
\n” _builder_version=”4.10.8″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”28px” custom_padding=”|0px||4px|false|false” disabled=”on” global_colors_info=”{}”]<\/p>\n

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

Q1<\/strong>. Find the value of a and b when a<\/span>3<\/span> \u00d7 b<\/span>3<\/span> = 12<\/span>3<\/span>.<\/span><\/p>\n

Sol.<\/strong> We know that the value of the cube of 12 = 1728<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0To find the value of a and b, we need to do the prime factorisation of 1728.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0The prime factorisation of 1728 = 2\u00d72\u00d72\u00d72\u00d72\u00d72\u00d73\u00d73\u00d73<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0We will make the pair of threes – 2<\/span>3<\/span>\u00d72<\/span>3<\/span>\u00d73<\/span>3<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0You can see that we have to find the value of a and b, but we are getting three pairs.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0We will use the identity – x<\/span>m<\/span>\u00d7y<\/span>m<\/span> = (xy)<\/span>m<\/span>.\u00a0<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Using the above formula we can write 1728 = (2\u00d72)<\/span>3<\/span> \u00d7 3<\/span>3<\/span>.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0The value of a<\/span>3<\/span> \u00d7 b<\/span>3<\/span> = 4<\/span>3<\/span>\u00d73<\/span>3<\/span>,<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0if a=4, then b=3\u00a0<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Or\u00a0 \u00a0 if a=3, then b=4.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0We can also write 1728 = (2\u00d73)<\/span>3<\/span> \u00d7 2<\/span>3<\/span>= 6<\/span>3<\/span>\u00d72<\/span>3<\/span>.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Here, a<\/span>3<\/span> \u00d7 b<\/span>3<\/span> = 6<\/span>3<\/span>\u00d72<\/span>3<\/span>, if a=6, then b=2 or if a=2, then b=6.<\/span><\/p>\n

Q2.<\/strong> When the cube of 12 is divided by the cube of 6, we get the cube of which number?<\/span><\/p>\n

Ans<\/strong>. The values of the cube of 6 and 12 are 216 and 1728 respectively.<\/span><\/p>\n

When 1728 is divided by 216 =<\/span> 1728<\/span>216<\/span>= 8.<\/span><\/p>\n

The prime factors of 8 are 2\u00d72\u00d72 = 2<\/span>3<\/span>.<\/span><\/p>\n

On applying the cube root on 2<\/span>3<\/span>, we get 2 as the cube root of 8.<\/span><\/p>\n

Therefore, when the cube of 12 is divided by the cube of 6, we get the cube of 2.<\/span><\/p>\n<\/div>\n<\/div>\n

[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” locked=”off” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics
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Explore Other Topics<\/h1>\n

[\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\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
Cube of 5<\/a><\/div>\n
Cubes from 1 to 30<\/a><\/a><\/div>\n<\/div>\n

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Frequently Asked Questions<\/h1>\n

Q1.<\/strong> Is the cube of 12 irrational?<\/span>
\nAns.<\/strong> The value of the cube of 12 is 1728, which is a rational number as it can be written in the form of <\/span>p\/<\/span>q <\/span>and q\u22600. Therefore, the cube of 12 is not an irrational number.\u00a0<\/span><\/p>\n

Q2.<\/strong> How many real and complex cube roots does a real number have? What is the real cube root of 1728?<\/span>
\nAns.<\/strong> A real number has one real cube root and two complex cube roots. The real cube root of 1728 is 12.<\/span><\/p>\n

Q3.<\/strong> Is it possible that the cube of an odd number is an even number?<\/span>
\nAns<\/strong> No, it is not possible that the cube of an odd number is an even number. It must be noted that the cube of an odd number will be an odd number and the cube of an even number will be an even number. We have seen that 12, which is an even number has the cube 1728, which is also an even number.\u00a0\u00a0\u00a0\u00a0<\/span>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

The value of the cube of 12 is 1728. The exponential form of a cube is x3. This can be found out by using the multiplication method and algebraic expressions.<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":714,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"yoast_head":"\nCube of 12- Value and methods to find it - mydomain<\/title>\n<meta name=\"description\" content=\"The value of the cube of 12 is 1728. The exponential form of a cube is x3. 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