{"id":1947,"date":"2021-09-15T13:54:54","date_gmt":"2021-09-15T13:54:54","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=1947"},"modified":"2021-12-31T11:09:07","modified_gmt":"2021-12-31T11:09:07","slug":"square-root-of-12-value-simplification-and-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/square-root-of-12-value-simplification-and-examples\/","title":{"rendered":"Square root of 12 – Value, simplification and examples"},"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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Square root of 12 – Value, simplification and examples<\/h1>\n

[\/et_pb_text][et_pb_text _builder_version=”4.11.3″ _module_preset=”default” text_font_size=”16px” custom_padding=”|15px||4px|false|false” global_colors_info=”{}”]<\/p>\n

This article will help you understand the value, simplification, and calculation of\u221a12. Later, we will help you solve some real-life applications of \u221a12 by using its value. So, let\u2019s get started; we have a lot of things to share.<\/p>\n

Definition of root 12<\/b><\/span><\/h2>\n

We know that we can find the square of a number by multiplying it twice with itself. Similarly, we can find the square root by inversing the operation of squaring. This means that 12 = a x a = a2<\/sup> and vice versa, a2<\/sup> = a x a = 12, where a is the quantity that represents the value of root 12. The mathematical representation of root 12 is given by \u221a12 in radical form. It can also be written as 2\u221a3.<\/p>\n

Is root 12 a rational number?<\/b><\/span><\/h2>\n

If 12 is a perfect square, then the square root of 12 is also a rational number. But, we know that 12 is not a perfect square. Therefore, the value of \u221a12 cannot be a rational number. This also means that the value of root 12 will be an infinite number that doesn\u2019t terminate after the decimal point, and you won\u2019t be able to write it in a fractional form.<\/p>\n

So, \u221a12 is an irrational number.<\/p>\n

How to find the value of \u221a12?<\/b><\/span><\/h2>\n

We can find the value of root 12 by prime factorization.<\/p>\n

First, let us write the factors of 12,
12 = 2 x 2 x 3<\/p>\n

For, \u221a12, we can write these factors as
\u221a12 = \u221a(2 x 2 x 3) = \u221a(22<\/sup> x 3) = 2\u221a3<\/p>\n

Now, put the value of \u221a3 = 1.732 so that we get
\u221a12 = 2 x 1.732
\u221a12 = 3.464
The value of \u221a12 can be both positive and negative, but here in this article we will only consider the positive value of root 12.<\/p>\n

The digits after the decimal point are never-ending, and they continue up to many places. The value of root 12 up to 10 decimal places is 3.4641016151<\/p>\n

Table of square roots from 1 to 15<\/span><\/strong><\/h2>\n

To make things easier for you, we are enlisting a table of square root values from 1 to 15. This table will come in handy while solving calculations and length problems.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Number<\/span><\/b>\u00a0<\/span><\/td>\nSquare Root<\/span><\/b>\u00a0<\/span><\/td>\n<\/tr>\n
1<\/span>\u00a0<\/span><\/td>\n1<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
2<\/span>\u00a0<\/span><\/td>\n1.414<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
3<\/span>\u00a0<\/span><\/td>\n1.732<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
4<\/span>\u00a0<\/span><\/td>\n2<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
5<\/span>\u00a0<\/span><\/td>\n2.236<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
6<\/span>\u00a0<\/span><\/td>\n2.449<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
7<\/span>\u00a0<\/span><\/td>\n2.646<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
8<\/span>\u00a0<\/span><\/td>\n2.828<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
9<\/span>\u00a0<\/span><\/td>\n3<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
10<\/span>\u00a0<\/span><\/td>\n3.162<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
11<\/span>\u00a0<\/span><\/td>\n3.317<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
12<\/span>\u00a0<\/span><\/td>\n3.464<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
13<\/span>\u00a0<\/span><\/td>\n3.606<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
14<\/span>\u00a0<\/span><\/td>\n3.742<\/span>\u00a0<\/span><\/td>\n<\/tr>\n
15<\/span>\u00a0<\/span><\/td>\n3.873<\/span>\u00a0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Solved examples:<\/span><\/strong><\/h2>\n

Question 1<\/strong> – Find the value of 3\u221a12 + 6\u221a3
Solution –<\/strong>\u00a0 Given, 3\u221a12 + 6\u221a3
We know that \u221a12 = 3.464 and \u221a3 = 1.732
Putting these values in the given equation,
= 3 x 3.464 + 6 x 1.732
= 10.392 + 10.392
= 20.784<\/p>\n

Question 2<\/strong> – Find the radius of a circle if its area is 12\u03c0 cm2<\/sup>
Solution<\/strong> – Given, the area of the circle = 12\u03c0 cm2<\/sup>
Now, area = \u03c0r2<\/sup> where, r is the radius of the circle.<\/p>\n

So,
\u03c0r2<\/sup> = 12\u03c0 cm2<\/sup>
We get, r2<\/sup> = 12 cm2<\/sup>
r = \u221a12 cm2<\/sup>
Putting the value of \u221a12 in the above equation,
We get, r = 3.464 cm<\/p>\n

Therefore, the radius of the circle is 3.464 cm.<\/p>\n

Question 3<\/strong> – Simplify 3\u221a12 + 2\u221a3
Solution –\u00a0 <\/strong>We have 3\u221a12 + 2\u221a3
Here, we can simplify \u221a12 as 2\u221a3
So, 3 (2\u221a3) + 2\u221a3
= 6 \u221a3 + 2 \u221a3
Taking \u221a3 as a common from both terms,
We get (6+2) \u221a3
So, the simplification of (3\u221a12 + 2\u221a3) gives 8\u221a3<\/p>\n

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Explore Other Topics<\/h1>\n

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Related Concepts<\/h1>\n

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\n
Root 5<\/a><\/div>\n
Root 7<\/a><\/div>\n
Root 10<\/a><\/div>\n<\/div>\n

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Frequently Asked Questions<\/h1>\n

1.<\/strong> Express the square root of 12 in radical form and exponent form.
Ans:<\/strong> The radical form of root 12 is given by \u221a12, and the exponent form is 121\/2<\/sup><\/p>\n

2.<\/strong> Is \u221a12 rational or irrational?
Ans:<\/strong> If 12 is a perfect square, then the square root of 12 is also a rational number. But, we know that 12 is not a perfect square. Therefore, the value of \u221a12 cannot be a rational number. This also means that the value of root 12 will be an infinite number that doesn\u2019t terminate after the decimal point, and you won\u2019t be able to write it in a fractional form.<\/p>\n

So, \u221a12 is an irrational number.<\/p>\n

3.<\/strong> Is 12 a perfect square?
Ans:<\/strong> No, 12 is not a perfect square.<\/p>\n

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

The square root of 12 is 3.464. We can find this by the prime factorization method. So let\u2019s dive in and learn more about \u221a12, its value and simplification. <\/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":"\nSquare root of 12 - Value, simplification and examples - mydomain<\/title>\n<meta name=\"description\" content=\"The square root of 12 is 3.464. We can find this by the prime factorization method. 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