{"id":2589,"date":"2021-10-05T04:42:27","date_gmt":"2021-10-05T04:42:27","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2589"},"modified":"2022-01-02T07:07:15","modified_gmt":"2022-01-02T07:07:15","slug":"cube-root-of-27-by-the-prime-factorisation-method","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/cube-root-of-27-by-the-prime-factorisation-method\/","title":{"rendered":"Cube root of 27 by the 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=”4.10.8″ _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
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Cube root of 27 by the 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=”{}”]<\/p>\n

When the number is multiplied three times by itself, the resultant number is the cube of that number and the cube root is the inverse of the cube i.e., the number which is multiplied three times by itself is the cube root. In this article, we are going to learn about the cube root of 27 and the prime factorisation method to find the cube root of 27.<\/p>\n

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Cube root<\/strong><\/h2>\n

 <\/p>\n

Introduction<\/strong><\/h3>\n

The cube of a number is equal to the number obtained by multiplying three times by itself. For example the cube of 2 is 8( as 2 x 2 x 2 =8). Similarly, the cube root of a number is that factor that is multiplied three times by itself to obtain that number. For example, the cube root of 8 is 2 (as 2, when multiplied three times by itself, gives 8).<\/p>\n

 <\/p>\n

Method of finding the cube root<\/strong><\/h2>\n

 <\/p>\n

PRIME FACTORISATION METHOD<\/strong><\/h3>\n

 <\/p>\n

The prime factorization method is the method of finding the cube root by using its prime factors. The following steps are to be followed to find the cube root of a number by using the prime factorization method-.<\/p>\n

 <\/p>\n

~Choose the number of which the cube root is to be found, Consider the number 27.<\/p>\n

 <\/p>\n

~ Divide 27 with the lowest prime number. Once the number ceases to be divisible by that first chosen prime number, choose another higher prime number and continue the process until the quotient thus obtained also results in a prime number.<\/p>\n

 <\/p>\n

 <\/p>\n\n\n\n\n\n
3<\/td>\n27<\/td>\n<\/tr>\n
3<\/td>\n9<\/td>\n<\/tr>\n
<\/td>\n3<\/td>\n<\/tr>\n<\/thead>\n<\/table>\n

 <\/p>\n

~Arrange the factors in groups of threes. Here, 27 – 3 x 3 x 3, which is 33<\/sup>.<\/p>\n

 <\/p>\n

~ Pick one number from each group and find their product, the product thus obtained is equal to the cube root of the number which is =\u00a0 \u221b27=\u00a0 \u221b33<\/sup> = 3.<\/p>\n

[\/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

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

Q1. Is 3 a rational number, whole number and integer?<\/span><\/p>\n

Ans. First of all, we will see whether it is a rational number or not. For rational number, we need to see whether it can be written in the form of <\/span>p\/<\/span>q<\/span> and q\u22600, so we can see that 3 can be written in the form of <\/span>p\/<\/span>q<\/span> and q\u22600. So, it is a rational number<\/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

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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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Cube and cube roots<\/a><\/div>\n
How to find the cube roots of a number easily?<\/a><\/div>\n
Cube root by long division method<\/a><\/div>\n

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Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n

Q1. Is 3 a rational number, whole number and integer?<\/span><\/p>\n

Ans. First of all, we will see whether it is a rational number or not. For rational number, we need to see whether it can be written in the form of <\/span>p\/<\/span>q<\/span> and q\u22600, so we can see that 3 can be written in the form of <\/span>p\/<\/span>q<\/span> and q\u22600. So, it is a rational number.<\/span><\/p>\n

We know that the whole numbers include 0 and all natural numbers. Therefore, 3 is a whole number. An integer contains all whole numbers as well as their negatives, so 3 is also an integer.<\/span><\/p>\n

Q2.\u00a0 Find the value of \u221b27a<\/span>12<\/sup><\/span>.<\/span><\/p>\n

Ans. We know that the cube root of 27 is 3.\u00a0<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0For a<\/span>12<\/span>, we can write it as a<\/span>4×3<\/span>, which is equal to\u00a0 (a<\/span>4<\/span>)<\/span>3<\/span> \u00a0 \u00a0 (By using identity a<\/span>mn<\/span> = (a<\/span>m<\/span>)<\/span>n<\/span>)<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0So, \u221b3<\/span>3<\/sup><\/span> x(a<\/span>4<\/sup><\/span>)<\/span>3<\/sup><\/span> = \u221b(3a<\/span>4<\/sup><\/span>)<\/span>3<\/sup><\/span> = 3a<\/span>4<\/sup><\/span>\u00a0 \u00a0 (By using identity a<\/span>n<\/span>xb<\/span>n<\/span> = (ab)<\/span>n<\/sup><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Therefore, the value of \u221b27a12<\/sup><\/span>\u00a0<\/span>is 3a<\/span>4<\/sup><\/span>.<\/span><\/p>\n

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