{"id":2274,"date":"2021-09-29T03:21:16","date_gmt":"2021-09-29T03:21:16","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2274"},"modified":"2021-12-31T11:16:17","modified_gmt":"2021-12-31T11:16:17","slug":"root-10-value-derivation-and-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/root-10-value-derivation-and-examples\/","title":{"rendered":"Root 10- Value, derivation 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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Root 10- Value, derivation and 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

The value of root 10\u00a0<\/b><\/h2>\n

Root 10 is denoted as \u221a10 in its radical form. Its square root (positive), rounded up to three decimal spaces, is 3.162.\u00a0<\/span><\/p>\n

 <\/p>\n

What are square roots\u00a0<\/b><\/h3>\n

The square root of a number is the value which, when multiplied by itself gives the original value. It is the inverse of squares.<\/span><\/p>\n

<\/h2>\n

About root 10\u00a0<\/b><\/h2>\n

The value of root 10 is an irrational number. The decimal form of \u221a10 is non terminating. At the same time, it is non-recurring. That means none of its digits in the decimal space ever repeat themselves nor can we see a pattern in their appearance.<\/span><\/p>\n

Here, we’re going to have a look at the methods of finding out the value of \u221a10.<\/span><\/p>\n

<\/h2>\n

Determining the value of \u221a10 using the long division method<\/b><\/h3>\n

The long division method is one of the most trusted ways of determining the root values of numbers. Here, we’ll follow these steps to find the square root of 10 by long division method:-<\/span><\/p>\n

Step 1<\/strong>:<\/span><\/p>\n

Make a pair of digits (by placing a bar over it) from the unit’s place and place this inside the radical symbol.<\/span><\/p>\n

Step 2:<\/strong><\/p>\n

We’ll now have to find a number such that when it is multiplied with itself, the product is less than or equal to 10<\/span><\/p>\n

We know that 3\u00b2 gives us 9 and 9 is less than 10. So it becomes our divisor.<\/span><\/p>\n

Step 3:<\/strong><\/p>\n

Next, we’ll place a decimal point and a pair of zeros next to 10 (dividend) and continue our division. Now, we multiply the quotient by 2 and the product becomes the starting digit of our next divisor.<\/span><\/p>\n

Step 4:<\/strong><\/p>\n

Now we’ll have to choose a number in the unit’s place for the new divisor such that its product with a number is less than or equal to 100.<\/span><\/p>\n

So, the closest multiplication we’re left with is 61 \u00d7 1 = 61<\/span><\/p>\n

Step 5:<\/strong><\/p>\n

We bring down the next pair of zeros and multiply the quotient by 2, and they become the two starting digits of the new divisor.<\/span><\/p>\n

Step 6:<\/strong><\/p>\n

Now, we choose a number in the unit’s place for the new divisor such that its product with a number is less than or equal to 3900. 3756 is the nearest number possible, leaving us with a remainder of 144.<\/span><\/p>\n

Step 7:<\/strong><\/p>\n

More pairs of zeros are added and the process is repeated to find the new divisor and product as in step 2. <\/span>Root 10 being irrational this division process is non terminating and will go on till ‘n’ number of terms.<\/span><\/p>\n

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

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

Illustrations<\/strong><\/h3>\n

1. Solve for x : 4x\u00b2 = 2x\u00b2 +20<\/span><\/p>\n

4x\u00b2- 2x\u00b2 = 20<\/span><\/p>\n

2x\u00b2 = 20<\/span><\/p>\n

x\u00b2 = 10 x= \u221a10<\/span><\/p>\n

Therefore, x = <\/span>\u00b1<\/span>3.162 (truncated)<\/span><\/p>\n

2. Find the value of \u221a10<\/span><\/p>\n

\u221a10 can be simplified as = \u221a(2×5)<\/span><\/p>\n

We know, \u221a2 = 1.414 and\u00a0 \u221a5 = 2.23<\/span><\/p>\n

So,\u00a0<\/span><\/p>\n

\u221a10 = 1.414 x 2.23<\/span><\/p>\n

Therefore,\u00a0<\/span><\/p>\n

the value of \u221a10 = 3.162<\/span><\/p>\n

[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics
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Explore Other Topics<\/h1>\n

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Geometry<\/a><\/div>\n
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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
Square and Square roots<\/a><\/div>\n
Root 7<\/a><\/div>\n
Square root of 20<\/a><\/div>\n<\/div>\n

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Frequently Asked Questions<\/h1>\n

1.<\/strong> What is the approximate value of root 10?<\/span><\/p>\n

Ans:<\/strong> The approximate value of root 10, up to three decimal places is 3.162<\/span><\/p>\n

2.<\/strong> What is the Principal Square Root of 10?<\/span><\/p>\n

Ans:<\/strong> The positive square root of 10 is called the principal square root of 10.<\/span><\/p>\n

3.<\/strong> Why is root 2 called a surd?<\/span><\/p>\n

Ans:<\/strong> \u221a2 cannot be simplified further without changing the number inside the radical sign into a fraction, so it is called a surd. Surds are the roots that cannot be simplified further.<\/span><\/p>\n

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

The truncated value of root 10 is 3.162. This value can be calculated using the long division method and the prime factorisation method; let\u2019s see how!<\/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":"\nRoot 10- Value, derivation and examples - mydomain<\/title>\n<meta name=\"description\" content=\"The truncated value of root 10 is 3.162. 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