{"id":6889,"date":"2021-12-28T07:56:38","date_gmt":"2021-12-28T07:56:38","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=6889"},"modified":"2022-01-03T06:44:21","modified_gmt":"2022-01-03T06:44:21","slug":"cube-root-of-1-to-20-definition-values-and-faqs","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/cube-root-of-1-to-20-definition-values-and-faqs\/","title":{"rendered":"Cube root of 1 to 20 – definition, values, and FAQs"},"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 1 to 20 – definition, values, and FAQs<\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

Before we get into the value of the cube root from 1 to 20, let us understand what a cube root is and how to calculate the cube roots of a perfect cube. A cube is a value we get when we multiply a number by itself three times.\u00a0<\/span><\/p>\n

For example, 3^{3}=3 \\times 3 \\times 3=27 . \\text { So, } 27 \\text { is the cube of } 3<\/span><\/span><\/p>\n

The cube root of a number is the value which when multiplied by itself three times, gives the original number.\u00a0<\/span><\/p>\n

For example, the cube root of 27, denoted as \u221b27, is 3 i.e. the number which when multiplied by itself three times gives 27.\u00a0<\/span><\/p>\n

So, 27 is the cube of 3, and 3 is the cube root of 27.<\/span><\/span><\/p>\n

In this article let us understand how to calculate the cube roots of perfect cubes, how to calculate the cube roots using the simple calculator, and the value of the cube roots of the numbers 1-20.\u00a0<\/span><\/p>\n

 <\/p>\n

Value of the cube root of 1 to 20 :<\/strong><\/h2>\n

It is recommended to memorize the cubes and cube roots of 1 to 20 as it would help the students to solve complex mathematical sums faster and easier.\u00a0 Cube roots are largely used in mensuration problems where the students are expected to find the length of a side and the volume of the object is given. The value of the cube roots of 1 to 20 is given here for the student\u2019s reference.\u00a0<\/span><\/p>\n

<\/span><\/p>\n

\"\"<\/span><\/p>\n

<\/span><\/p>\n

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

Prime factorization for calculating cube root:<\/strong><\/h2>\n

We can calculate the cube root of a perfect cube using prime factorization with relative ease. Let us understand this method with the help of an example.\u00a0<\/span><\/span><\/p>\n

Let us calculate the cube root of 3375.<\/span><\/p>\n

Step – 1<\/b>: Let us list out the prime factors of 3375 using the prime factorization method.<\/span><\/p>\n

\"\"<\/p>\n

<\/span><\/p>\n

Listing out the factors, we get <\/span>3375 = 3 \u2715 3 \u2715 3 \u2715 5 \u2715 5 \u2715 5<\/span>\u00a0<\/span><\/p>\n

<\/span><\/p>\n

Step – 2: <\/b>Consider the prime factor once every three times it is repeated. Thus, we get <\/span><\/p>\n

3 <\/span>\u2715 <\/span>5 <\/span>= 15 as the cube root.\u00a0<\/span><\/p>\n

 <\/p>\n

Solved Illustrations:<\/strong><\/h2>\n

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

1. Calculate the cube root of 729 using the prime factorization method.<\/b><\/p>\n

Solution:<\/b><\/p>\n

Listing out the prime factors of 729, we get 729 = 3 <\/span>\u2715 <\/span>3 <\/span>\u2715 <\/span>3 <\/span>\u2715 <\/span>3 <\/span>\u2715 <\/span>3 <\/span>\u2715 <\/span>3.<\/span><\/p>\n

Next, we shall <\/span>Consider the prime factor once every three times it is repeated. Since 3 is repeated 6 times, we get 3 <\/span>\u2715 <\/span>3 = 9<\/span> as the cube root of 729.<\/span><\/p>\n

 <\/p>\n

2. Find the value of \\sqrt[3]{12}+12^{3}<\/span>.<\/b><\/p>\n

Solution:<\/b><\/b><\/p>\n

From the above table, we know that the value of \u221b12 = 2.289.<\/span><\/p>\n12^{3}=12 \\times 12 \\times 12=1728<\/span>\n

So, the value of \\sqrt[3]{12}+12^{3} \\text { is } 2.289+1728=1730.289<\/span><\/span><\/p>\n

<\/span><\/p>\n

3. If the volume of a cube is 15 m<\/b>\u00b3<\/b>, find the length of the cube<\/b><\/b><\/p>\n

Solution:<\/b><\/p>\n

We know that the volume of a cube =a^{3}<\/span> <\/span>where a is the length of the cube.\u00a0<\/span><\/p>\n

\\text { So, } 15 {\\text{m}}^{3}=a^{3} <\/span><\/span><\/p>\n

a=\\sqrt[3]{15}<\/span><\/span><\/p>\n

a = 2.466 m<\/span><\/p>\n

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Explore Other Topics<\/h1>\n

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[\/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 cube root of a number easily<\/a><\/div>\n
Cube root of 4<\/a><\/a><\/div>\n<\/div>\n

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

    Q1. What is a perfect cube?
    <\/strong><\/h3>\n

    Ans: <\/strong>A perfect cube is any number whose cube root is a whole number without any decimal digits or fractions. For example, the cube root of 27 is 3 and the cube root of 17 is 2.571. Here, there are no decimal digits or fractions in the cube root of 27 and hence it is a perfect cube. However, there are decimal digits in the cube root of 17 and hence, it is not a perfect cube.
    <\/span><\/span><\/p>\n

    Q2. List down the steps to calculate the cube root using a simple calculator?
    <\/strong><\/h3>\n

    Ans: <\/strong>Follow the below-mentioned steps to calculate the cube root of any number using a simple calculator:
    Step -1: Enter the number in the calculator.
    Step – 2: Press the root ( \u221a ) button twice.
    Step – 3: Press the multiply ( \u2715) button.
    Step – 4: Press the root ( \u221a ) button four times.
    Step – 5: Press the multiply ( \u2715) button.
    Step – 6: Press the root ( \u221a ) button eight times.
    Step – 7: Press the multiply ( \u2715) button.
    Step – 8: Press the root ( \u221a ) button twice.
    Step – 9: Press the equal to ( =) button.<\/p>\n

    The resulting value is the cube root of the number. <\/p>\n

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

    [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

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