{"id":2503,"date":"2021-10-04T03:42:13","date_gmt":"2021-10-04T03:42:13","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2503"},"modified":"2022-01-02T07:19:47","modified_gmt":"2022-01-02T07:19:47","slug":"cube-root-of-729-by-prime-factorisation-method","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/cube-root-of-729-by-prime-factorisation-method\/","title":{"rendered":"Cube root of 729 by prime factorisation 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 729 by prime factorisation 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=”#7F7F7F” custom_padding=”15px|15px||4px|false|false” global_colors_info=”{}”]When we multiply a number three times by itself, the product is the cube of that number. The number is the cube root of the product. This means that the cube root is the inverse of the cube. The radical symbol of the cube root is \u221b. So, In this article, we will discuss the cube root of 729 and the prime factorisation method to find its cube root.<\/span><\/p>\n

CUBE ROOT OF 729<\/strong><\/h2>\n

The cube root of 729 is 9. It means that the product of 9 thrice by itself yields the number 729.\u00a0<\/span><\/p>\n

How to find the cube root?<\/strong><\/h3>\n

To find the cube root of a number, we can use the prime factorisation method. By evaluating the prime factors we will make the groups of threes of the same digits and then we apply the cube root and we get the cube root of the required number. This is the easiest method to find the cube root of any number.<\/span><\/p>\n

How to calculate the cube root of 729?<\/strong><\/h3>\n

The prime factors of 729 are 3\u00d73\u00d73\u00d73\u00d73\u00d73.\u00a0<\/span><\/p>\n

The groups of threes of the same values =<\/span><\/p>\n

33<\/sup>\u00d7<\/span>\u00a033<\/sup> = (3\u00d73)3<\/sup><\/span><\/p>\n

Therefore, the cube root of 729 by prime factorization is \u221b(3\u00d73)<\/span>3<\/span> =\u00a0 \u221b93<\/sup><\/span>\u00a0which is equal to 9.<\/span><\/p>\n

Illustration<\/span><\/h2>\n

Q1. a3<\/sup><\/span> + 386 = 93<\/sup><\/span>, find the value of a.<\/span><\/p>\n

Sol. We know that the value of 93<\/sup><\/span>\u00a0is equal to 729.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span> \u00a0So,\u00a0 a3<\/sup><\/span>\u00a0+ 386 = 729<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 a3<\/sup><\/span>\u00a0= 729 – 386<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 a3<\/sup><\/span>\u00a0= 343<\/span><\/p>\n

\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\u00a0a = \u221b343<\/span><\/p>\n

\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\u00a0a = \u221b(7\u00d77\u00d77)<\/span><\/p>\n

\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\u00a0a = \u221b7<\/span>3<\/sup><\/span><\/p>\n

\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\u00a0a = 7.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0Thus, the value of a is equal to 7.<\/span>[\/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

\n
\n

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

Q1. a<\/span>3<\/span> + 386 = 9<\/span>3<\/span>, find the value of a.<\/span><\/p>\n

Sol. We know that the value of 9<\/span>3<\/span> is equal to 729.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>\u00a0\u00a0So,\u00a0 a<\/span>3<\/span> + 386 = 729<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0a<\/span>3<\/span> = 729 – 386<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0a<\/span>3<\/span> = 343<\/span><\/p>\n

\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\u00a0a = \u221b343<\/span><\/p>\n

\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\u00a0a = \u221b(7\u00d77\u00d77)<\/span><\/p>\n

\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\u00a0a = \u221b7<\/span>3<\/span><\/p>\n

\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\u00a0a = 7.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0Thus, the value of a is equal to 7.<\/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” 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

\n
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 root by long division method<\/a><\/div>\n
Cube root of 343<\/a><\/a><\/div>\n<\/div>\n

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Frequently Asked Questions<\/h1>\n

Q1<\/strong>. Is 729 both the cube as well as square?<\/span>
\nAns.<\/strong> The prime factors of 729 are 3\u00d73\u00d73\u00d73\u00d73\u00d73, to find the square root, we will make the groups of twos of the same values. So, the groups = 32<\/sup><\/span>\u00d732<\/sup><\/span>\u00d732<\/sup><\/span>= (3\u00d73\u00d73)2<\/sup><\/span>, when we apply the square root, we get the number 27. We already know that the cube root of 729 is 9. So, 729 is the cube of 9 and the square of 27.<\/span><\/p>\n

Q2.<\/strong> Is 729 a perfect cube?<\/span>
\nAns.<\/strong> When we combine the prime factors of 729 in groups of threes, we get 33<\/sup><\/span> \u00d7 33<\/sup><\/span>\u00a0to which if we apply cube root, we get, 9. Hence, 729 is a perfect cube.<\/span><\/p>\n

Q3.<\/strong> What is the cube root of 729?<\/span>
\nAns<\/strong> The cube root of 729 is equal to 9. It means that when we multiply 9 thrice by itself, it will yield the product 729.<\/span>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

We will use the prime factorization method to get the cube root of 729.
\n The prime factors of 729 = \u221b(3\u00d73)3 = \u221b93, which is equal to 9.<\/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 root of 729 by prime factorisation method - mydomain<\/title>\n<meta name=\"description\" content=\"We will use the prime factorization method to get the cube root of 729. 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The prime factors of 729 = \\u221b(3\\u00d73)3 = \\u221b93, which is equal to 9\",\"breadcrumb\":{\"@id\":\"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/cube-root-of-729-by-prime-factorisation-method\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/cube-root-of-729-by-prime-factorisation-method\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/cube-root-of-729-by-prime-factorisation-method\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/stgwebsite.mindspark.in\/studymaterial\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Math Concepts\",\"item\":\"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Cube root of 729 by prime factorisation method\"}]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Cube root of 729 by prime factorisation method - mydomain","description":"We will use the prime factorization method to get the cube root of 729. 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