{"id":6181,"date":"2021-12-20T08:06:20","date_gmt":"2021-12-20T08:06:20","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=6181"},"modified":"2022-01-03T08:09:52","modified_gmt":"2022-01-03T08:09:52","slug":"square-root-tricks-with-examples-and-faqs","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/square-root-tricks-with-examples-and-faqs\/","title":{"rendered":"Square Root Tricks with Examples and FAQs"},"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=”4.10.8″ _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 Tricks with Examples and FAQs<\/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|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

Square Root Tricks<\/b><\/h2>\n

Before discussing the steps to make finding square roots easier, let\u2019s first define what are square roots.<\/span><\/p>\n

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

Square Roots<\/b><\/span><\/h3>\n

A number when multiplied to itself gives a number which is its square and the number itself is called the square root of the resulting number.<\/span><\/p>\n

The symbol to represent root is <\/span>\u221a<\/span> .\u00a0 The square root of a whole number can be a rational or irrational number. The numbers whose roots are a whole number are called perfect squares.<\/span><\/p>\n

The square roots of a number can have both positive and negative values, in this article we will discuss the tricks to find the positive roots.\u00a0<\/span><\/p>\n

For example, <\/span><\/p>\n

7 \u00d7 7 = 49 \u21d2 49 is the square of 7.<\/span>\u00a0<\/span><\/p>\n

(-<\/span>7) \u00d7 (-7) = 49 \u21d2 49 is the square of (-7).<\/span><\/p>\n

49 <\/span>= \u00b17 \u00a0 \u21d2\u00a0 \u00b17 is the square root of 49.<\/span><\/p>\n

We can also say that 49 is a perfect square.<\/span><\/p>\n

 <\/p>\n

Table of Squares of first 10 Natural Numbers<\/b><\/h3>\n

<\/b><\/p>\n

\"\"<\/p>\n

<\/b><\/p>\n

Table of Square Root of first 10 Natural numbers<\/b><\/h3>\n

<\/b><\/p>\n

\"\"<\/b><\/p>\n

<\/b><\/p>\n

Trick<\/b><\/h2>\n

The trick to find the square root of numbers that are greater than 100 are:<\/span><\/p>\n

1. First, start grouping up the digits from right to left, first in pair of two and the remaining another group.<\/span><\/p>\n

For example,<\/span><\/p>\n

If the number is a 3 digit number, let the number be 324: grouping is <\/span>3<\/b> 24<\/b>\u00a0<\/span><\/p>\n

If the number is a 4 digit number, let the number be 1764: grouping is <\/span>17<\/b> 64<\/b>\u00a0<\/span><\/p>\n

If the number is a 5 digit number, let the number be 12544: grouping is <\/span>125<\/b> 44<\/b>\u00a0<\/span><\/p>\n

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

2. The unit digit of the first pair from the right, is used to get an idea of the resulting numbers unit digit from the table below. Where the squares of the first 10 natural numbers are given with the unit\u2019s digit of each square.<\/span><\/p>\n

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

\"\"<\/p>\n

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

For example,<\/span><\/p>\n

If the number is 324 and its grouping is <\/span>3<\/b> 24<\/b>, now in the first pair from right we see that units digit is 4. We check from the table that the squares of 2 and 8 have 4 at their unit\u2019s place. So, the units place of the square root of 324 will be 2 or 8.<\/span><\/p>\n

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

3. The second group of the number is taken, and then we need to find two numbers from the list between the squares of which this number lies. The smaller of the two numbers is the ten\u2019s digit of the square root.<\/span><\/p>\n

For example,<\/span><\/p>\n

If the number is 324 and its grouping is <\/span>3<\/b> 24<\/b>, now from the second part we see that the number is 3. 3 lies between the squares of 1 and 2.<\/span><\/p>\n

1^{2}<3<2^{2}<\/span><\/span><\/p>\n

Now as <\/span>1 < 2, <\/span>hence the tens digit of the required square root is 1.<\/span><\/p>\n

Now the square root of <\/span>324 <\/span>can be either <\/span>12 or 18<\/span>.<\/span><\/p>\n

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

4. The product of the probable digits which can be at the tens place is taken. If the product value is greater than the second group from the right, the units digit of the square root is lesser of the two options available for the units\u2019 digit.<\/span><\/p>\n

And if it is lesser than or equal to the second part from the right it is the greater of the two options.<\/span><\/p>\n

In the example, we have been discussing already,<\/span><\/p>\n

1 \u00d7 2 = 2, <\/span><\/p>\n

2 \u2264 3,<\/span><\/p>\n

Hence the units digit is greater of the digits among 2 and 8,<\/span><\/p>\n\\sqrt{324}=18<\/span>\n

The following examples will make understanding the trick easier.<\/span><\/p>\n

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

Examples<\/b><\/h2>\n

Square root of a 3-digit Number<\/b><\/h3>\n

Find \\sqrt{576}<\/span>.<\/span><\/p>\n

Pairing the digits from right to left,\u00a0<\/span><\/p>\n

5<\/b> 76<\/b><\/p>\n

The unit digit of the number is 6 hence the unit digit of the square root will be 4 or 6.<\/span><\/p>\n

Now the number 5 lies between\u00a0<\/span><\/p>\n

2^{2}<5<3^{2}<\/span><\/span><\/p>\n

Hence the tens digit of the square root of 576 is 2 as 2 < 3.<\/span><\/p>\n

Therefore, the square root is either 24 or 26.<\/span><\/p>\n

Taking the products of possible tens digits <\/span>2 \u00d7 3 = 6,<\/span><\/p>\n

As 6 > 5, the units digit is the lesser of the two, among 4 and 6.<\/span><\/p>\n

\\sqrt{576}=24<\/span><\/span><\/p>\n

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

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

Square Root of a 4-digit Number<\/b><\/h3>\n\\text { Find } \\sqrt{1849} \\text {. }<\/span>\n

Pairing the digits from right to left,\u00a0<\/span><\/p>\n

18<\/b> 49<\/b><\/p>\n

The unit digit of the number is 9 hence the unit digit of the square root will be 3 or 7.<\/span><\/p>\n

Now the number 18 lies between\u00a0<\/span><\/p>\n

4^{2}<18<5^{2}<\/span><\/span><\/p>\n

Hence the tens digit of the square root of 1849 is 4 as 4 < 5.<\/span><\/p>\n

Therefore, the square root is either 43 or 47.<\/span><\/p>\n

Taking the products of possible tens digits <\/span>4 \u00d7 5 = 20,<\/span><\/p>\n

As 20 > 18, the units digit is the lesser of the two, among 3 and 7.<\/span><\/p>\n

\\sqrt{1849}=43<\/span><\/span><\/p>\n

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

Square Root of a 5-digit Number<\/b><\/h3>\n

\\text { Find } \\sqrt{28224}<\/span><\/b>.<\/p>\n

Pairing the digits from right to left,\u00a0<\/span><\/p>\n

282<\/b> 24<\/b><\/p>\n

The unit digit of the number is 4 hence the unit digit of the square root will be 2 or 8.<\/span><\/p>\n

Now the number 262 lies between\u00a0<\/span><\/p>\n

16^{2}<282<17^{2}<\/span><\/span><\/p>\n

Hence the first two digits of the square root of 28224 are 16 as 16 < 17.<\/span><\/p>\n

Therefore, the square root is either 162 or 168.<\/span><\/p>\n

Taking the products of possible first two digits <\/span>16 \u00d7 17 = 272,<\/span><\/p>\n

As 272 <\/span> 282, the units digit is the greater of the two, among 2 and 8.<\/span><\/p>\n

\\sqrt{28224}=168<\/span><\/span><\/p>\n

<\/b><\/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

[\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n

\n
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
Square and Square roots<\/a><\/div>\n
Square roots between 1 to 50<\/a><\/div>\n
Root 5<\/a><\/a><\/div>\n<\/div>\n

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Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n
    <\/ol>\n

    Q1.\u00a0 What do you mean by square root?
    <\/strong><\/h3>\n

    Ans: <\/strong>A number when multiplied to itself gives a number which is its square and the number itself is called the square root of the resulting number. The symbol to represent root is \u221a .
    For example,
    9 \u00d7 9 = 81 \u21d2 81 is the square of 9.
    \\sqrt{81}=9 \\Rightarrow 9<\/span> is the square root of 81.
    <\/span><\/span><\/p>\n

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

    Q2. Are square roots always whole numbers?
    <\/strong><\/h3>\n

    Ans: <\/strong>No, the square root of a number can be a whole, rational or irrational number.<\/span><\/p>\n

    When it\u2019s a whole number then the number is a perfect square. The Square roots can also be negative as the product of two negative numbers yields a positive number.<\/span><\/p>\n

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

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