{"id":2225,"date":"2021-09-28T11:35:08","date_gmt":"2021-09-28T11:35:08","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2225"},"modified":"2021-12-31T11:18:48","modified_gmt":"2021-12-31T11:18:48","slug":"square-root-of-144-value-derivation-and-solved-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/square-root-of-144-value-derivation-and-solved-examples\/","title":{"rendered":"Square root of 144 – value, derivation and solved 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
\n” _builder_version=”4.13.1″ _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

Square root of 144 – value, derivation and solved examples<\/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=”#777777″ custom_padding=”15px|15px||4px|false|false” global_colors_info=”{}”]<\/p>\n

In mathematics, we can calculate the square root of a number by inverting the squaring operation. For instance, the value of the square root of 144 is 12 because 12 x 12 gives 144. We can also write this equation in radical form as \u221a144 = 12. The preceding equation shows that the natural number 144 gives a square root of 12. This is a value that gives the number 144 when multiplied by itself.<\/p>\n

Don\u2019t worry; if you can\u2019t remember this, we\u2019ll share two methods to calculate the value of \u221a144 \u2013 prime factorisation and long division.\u00a0 In this article, we will learn both methods and look at some solved examples to strengthen your understanding of the concept of square roots.<\/p>\n

What does the square root of a number mean?\u00a0\u00a0\u00a0<\/strong><\/h2>\n

A value expressed by x = \u221aa represents the square of any natural integer. It means that x, where a is any natural integer, is the square root of a. Thus, it is inferred that the square root of any number is identical to a figure that gives the original numbers when multiplied by itself. For instance, 4 x 4 = 16, and the root of the square of the number 16 may be stated to be 4. The symbol \u2018\u221a\u2019 represents a square root and is also called \u2018radical\u2019.<\/p>\n

How to find the value of the square root of 144 by prime factorisation?<\/strong><\/h3>\n

To find the value of \u221a144 by prime factorisation, follow the steps mentioned below:<\/p>\n

    \n
  1. First, calculate the prime factors of 144 and write them down.
    144 = 2 x 2 x 2 x 2 x 3 x 3<\/li>\n
  2. Group these prime factors in a pair of two factors each.
    144 = 22<\/sup> x 22<\/sup> x 32<\/sup><\/li>\n
  3. Add a square root on both sides.
    \u221a144 = \u221a(22<\/sup> x 22<\/sup> x 32<\/sup>)
    \u221a144 = \u221a(2 x 2 x 3)2<\/sup>
    \u221a144 = (2 x 2 x 3)2 x \u00bd
    <\/sup>\u221a144 = 12<\/li>\n<\/ol>\n

    By following these steps, you can calculate the prime factors of \u221a144 within no time.<\/p>\n

    Finding the value of \u221a144 by long division<\/strong><\/h3>\n

    We may also use the long division approach to determine the square root of any number. This approach is highly beneficial and the fastest way to discover the root. The root of the imperfect squares and of big numbers cannot be found by prime factorisation, but long division comes to the rescue here. The instructions below are for applying long division to find the value of \u221a144.<\/p>\n

    \"\"<\/p>\n

     <\/p>\n

      \n
    1. As indicated in the image, write 144. Start by placing a bar above it, grouping the number in pairs of two digits from the right. The left unpaired number can be regarded as a single entity. For instance, for the number 144, 44 has one bar above it, and 1 has the second.<\/li>\n
    2. We know that digit 1’s square root is always 1. Therefore, given that 1 is the quotient, dividend and divisor, the remainder equals 0.<\/li>\n
    3. Now, we’re going to bring down the next two numbers as a dividend, i.e. 44, and add 1 to our next divisor, i.e. 1+1 =2.<\/li>\n
    4. Select a number for the unit place of the divisor to yield 44 or a smaller number closest to 44 when multiplied by the new divisor. The number is 22 since 22 x2 = 44 here.<\/li>\n<\/ol>\n

      Solved examples<\/strong><\/h3>\n
        \n
      1. Find the square root of 81 by prime factorisation.<\/li>\n<\/ol>\n

        Follow the steps below to find the value of \u221a81<\/p>\n