{"id":2517,"date":"2021-10-04T03:59:39","date_gmt":"2021-10-04T03:59:39","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2517"},"modified":"2022-01-02T07:18:41","modified_gmt":"2022-01-02T07:18:41","slug":"values-of-cubes-of-numbers-from-1-to-30","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/values-of-cubes-of-numbers-from-1-to-30\/","title":{"rendered":"VALUES OF CUBES OF NUMBERS FROM 1 TO 30"},"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
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VALUES OF CUBES OF NUMBERS FROM 1 TO 30<\/strong><\/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|||||||” header_3_text_color=”#777777″ custom_padding=”15px|15px||4px|false|false” global_colors_info=”{}”]<\/p>\n

When a number is raised to the power 3, it is called the cube of a number. We cannot memorise the cube of every number. It is good if we learn the cubes of some numbers. In this article, we are going to discuss the values of cubes from 1 to 30.<\/span><\/p>\n

<\/h2>\n

Values of cubes from 1 to 30<\/strong><\/h2>\n

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

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

<\/h2>\n

How to find the cube of the number?<\/strong><\/h2>\n

To find the cube of a number, we can multiply it three times by itself.<\/span><\/p>\n

For eg- 8^3=8\\times 8\\times 8=512<\/span>.<\/span><\/p>\n

We can also find the cube with the help of the following expression –<\/span><\/p>\n

(p+q)^3=p^3+q^3+3pq(p+q) \\text{ or } (p-q)^3=p^3-q^3-3pq(p-q)<\/span><\/span><\/p>\n

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

We can write 8 as (6 + 2), here- p = 6, q = 2<\/span><\/p>\n

Using the first expression,\u00a0<\/span><\/p>\n

(6+2)^3=6^3+2^3+3\\times 6\\times 2(6+2)<\/span><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 216 + 8 + 36 \u00d7 8\u00a0\u00a0<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 224 + 288<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 512<\/span><\/p>\n

We can also write 8 as (10 – 2) where p = 10 & q = 2.<\/span><\/p>\n

Using the second expression,<\/span><\/p>\n

(10-2)^3=10^3-2^3-3\\times 10\\times 2(10-2)<\/span><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 1000 – 8 – 60 \u00d7 8<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 1000 – 8 – 480<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 512<\/span><\/p>\n

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

Solved Questions<\/strong><\/h2>\n

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

Q1. What is the value of 7^3+8^3+9^3<\/span>?<\/strong><\/p>\n

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

We know the cube of 7, 8 and 9 are 343, 512 and 729 respectively.<\/span><\/p>\n

So, the value is:<\/span><\/p>\n

7^3+8^3+9^3=343+512+729=1584<\/span><\/span><\/p>\n

 <\/p>\n

Q2. Subtract three times the cube of 19 from 2 times the cube of 25.<\/strong><\/p>\n

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

We need to subtract 3\\times 19^3 \\text{ from }2\\times 25^3<\/span>.<\/span><\/p>\n

25^3=15625\\text{ and } 19^3=6859<\/span><\/span><\/p>\n

\\therefore 2\\times 25^3- 3\\times 19^3=2\\times 15625-3\\times 6589<\/span><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 31250 – 20577\u00a0<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 10673<\/span><\/p>\n

Q3. By what number should we multiply the cube of 2 to get the cube of 4?<\/strong><\/p>\n

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

We know that, 2^3=8\\text{ and }4^3=64<\/span><\/span><\/p>\n

Let the number to be found is \u2018x\u2019.<\/span><\/p>\n

8x = 64<\/span><\/p>\n

\u00a0x = 8<\/span><\/p>\n

Hence cube of 2 should be multiplied by 8(i.e., cube of 2 itself) to get the cube of 4.<\/span><\/p>\n

<\/span><\/p>\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
Cube of 5<\/a><\/div>\n
Cube of 12<\/a><\/div>\n<\/div>\n

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Frequently Asked Questions<\/h1>\n

Q1<\/strong>. Which of the numbers from 1 to 30 are prime, odd and even?<\/strong><\/span>
Ans.<\/strong> The number which is only divided by itself and 1 is called a prime number. The prime numbers start with 2 and so on. \u20181\u2019 is not a prime number because it has only one positive factor.<\/span>
In 1 to 30, the prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.<\/span>
An odd number is a number which when divided by 2 leaves the remainder 1. The exception to this definition is \u20181\u2019. Cubing an odd number yields an odd number.<\/span>
In 1 to 30, the odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29.<\/span>
An even number is a number that is totally divisible by 2. Cubing an even number yields an even number.<\/span>
In 1 to 30, the even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30.<\/span><\/p>\n

Q2.<\/strong> What is the formula of a perfect cube?<\/strong><\/span>
Ans<\/strong>. The formula of a perfect cube = n^3<\/span><\/span>, where n is any number. For eg- When we multiply the number 7 thrice by itself, it will yield the result 343. Therefore, 343 is a perfect cube.<\/span><\/p>\n

Q3.<\/strong> Is 64 both a perfect cube and a perfect square?<\/strong><\/span>
Ans.<\/strong> The prime factors of 64 = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2. When we form the groups of the same values of the prime factors into triplets we get, (2^3\\times 2^3)\\text{ which equals to }(2\\times 2)^3<\/span><\/span>. On applying the cube root on (2\\times 2)^3<\/span><\/span>, we get 4 as the cube root of 64.<\/span><\/p>\n

When we form the groups of twos of the same digits of the prime factors of 64, we get <\/span><\/p>\n

(2^2\\times 2^2\\times 2^2)\\text{ which equals to }(2\\times 2\\times 2)^2<\/span><\/span>. On applying the square root on (2\\times 2\\times 2)^2<\/span><\/span>, we get 8 as the square root of 64. <\/span>Therefore, 64 is both a perfect cube and a perfect square.<\/span><\/p>\n

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