{"id":2219,"date":"2021-09-28T10:50:42","date_gmt":"2021-09-28T10:50:42","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2219"},"modified":"2021-12-31T11:05:19","modified_gmt":"2021-12-31T11:05:19","slug":"square-root-of-100-value-and-solved-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/square-root-of-100-value-and-solved-examples\/","title":{"rendered":"Square root of 100 – value 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 100 – value and solved examples<\/b><\/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=”{}”]100 is a perfect square of 10. We can say this because 10 when multiplied by itself, gives 100. Furthermore, 100 is also a rational number. This article will elaborate upon the value of the square root of 100 and its derivation by the prime factorisation method. So, buckle up, and let\u2019s start learning. At the end of this article, we will share some solved examples to make you aware of the mathematical applications of <\/span>\u221a100.<\/span><\/p>\n

Let\u2019s get started.<\/span><\/p>\n

Square root of 100<\/b><\/h2>\n

10 is the square root of 100 because we know that 10 x 10 gives 100. Hence, upon inversing the operation, we get <\/span>\u221a100 = <\/span>\u00b1<\/span>10. The value of \u221a100 is positive or negative but in this article we will consider the positive value only.<\/span><\/p>\n

How to calculate the square root of 100?<\/b><\/p>\n

While there are many ways to find the value of a square root, in this article, we will focus on the prime factorisation method to derive the value of <\/span>\u221a10<\/span>. Furthermore, we know that 100 is a perfect square number, so we can successfully calculate its square root using the prime factorisation method. 100 is a composite number because it has more than two factors. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100<\/span><\/p>\n

Now, we will use prime factorisation to calculate the factors of <\/span>\u221a100.<\/span><\/p>\n

Upon factorisation, we get 100 = 2 x 2 x 5 x 5.\u00a0<\/span><\/p>\n

So, <\/span>\u221a100 = \u221a(<\/span>2 x 2 x 5 x 5)<\/span><\/p>\n

The factors include two pairs of the number 2 and two pairs of the number 5; therefore, we can consider each pair as one number to do away with the square root.<\/span><\/p>\n

\u221a100 = <\/span>2 x 5\u00a0<\/span><\/p>\n

\u221a100 = 10<\/span><\/p>\n

100 is a perfect square and 10 x 10 = 100. So, we can also find the root of 100 by another method, i.e., by inversing the squaring operation.\u00a0<\/span><\/p>\n

\u221a100 = \u221a10<\/span>2<\/sup><\/span><\/p>\n

= 102*(1\/2)<\/sup><\/span><\/p>\n

= 10<\/span><\/p>\n

So, \u221a100 is 10\u00a0\u00a0<\/span><\/p>\n

Let us look at the root in correlation with power.<\/span><\/p>\n

Consider the number’ a’ and a natural number ‘x.’\u00a0<\/span><\/p>\n

Then, a<\/span>x<\/sup><\/span> = a * a * a \u2026\u2026 (multiplied ‘x’ number of times)<\/span><\/p>\n

If the value of \u2018x\u2019 is 2 and \u2018a\u2019 is 4, then 4<\/span>2<\/span> = 4 x 4 = 16<\/span><\/p>\n

This means, ‘4 raised to the power 2’ is 16.<\/span><\/p>\n

Now, the root is the inverse of power. Therefore, we can also see that 10, when multiplied by itself, gives 100. Hence, if 100 is the square of 10 then 10 is also the square root of 100.<\/span><\/p>\n

Is \u221a100 a rational or irrational number?<\/b><\/p>\n

If a number terminates at some point or has a repeating pattern in its decimal part, then it is a rational number. Here, we can see that the value of \u221a100 is 10, i.e., a whole number. Hence, it is a rational number<\/span><\/p>\n

Facts worth considering<\/b><\/h3>\n