[/et_pb_text][et_pb_text _builder_version=”4.1″ text_font=”Raleway||||||||” text_font_size=”20px” text_letter_spacing=”1px” text_line_height=”1.5em” background_color=”#f4f4f4″ custom_margin=”10px||10px” custom_padding=”10px|20px|10px|20px” box_shadow_style=”preset2″]Competency in Focus: Perfect square numbers This problem from American Mathematics contest (AMC 10A, 2014) is based on the concept that when a number is a perfect square .
[/et_pb_text][et_pb_text _builder_version=”3.27.4″ text_font=”Raleway|300|||||||” text_text_color=”#ffffff” header_font=”Raleway|300|||||||” header_text_color=”#e2e2e2″ background_color=”#0c71c3″ custom_padding=”20px|20px|20px|20px” border_radii=”on|5px|5px|5px|5px” box_shadow_style=”preset3″]
[/et_pb_text][et_pb_text _builder_version=”4.1″ text_font=”Raleway||||||||” text_font_size=”20px” text_letter_spacing=”1px” text_line_height=”1.5em” background_color=”#f4f4f4″ custom_margin=”10px||10px” custom_padding=”10px|20px|10px|20px” hover_enabled=”0″ box_shadow_style=”preset2″]Which of the following numbers is a perfect square? [/et_pb_text][/et_pb_column][/et_pb_row][et_pb_row _builder_version=”4.0″][et_pb_column type=”4_4″ _builder_version=”3.25″ custom_padding=”|||” custom_padding__hover=”|||”][et_pb_accordion open_toggle_text_color=”#0c71c3″ _builder_version=”4.1″ toggle_font=”||||||||” body_font=”Raleway||||||||” text_orientation=”center” custom_margin=”10px||10px” hover_enabled=”0″][et_pb_accordion_item title=”Source of the problem” open=”on” _builder_version=”4.1″ hover_enabled=”0″]American Mathematical Contest 2014, AMC 10A Problem 8
[/et_pb_accordion_item][et_pb_accordion_item title=”Key Competency” _builder_version=”4.1″ hover_enabled=”0″ open=”off”]This number theory problem is based on the concept that when a number is a perfect square
[/et_pb_accordion_item][et_pb_accordion_item title=”Difficulty Level” _builder_version=”4.1″ hover_enabled=”0″ open=”off”]5/10
[/et_pb_accordion_item][et_pb_accordion_item title=”Suggested Book” _builder_version=”4.0.9″ open=”off”]Challenges and Thrills in Pre College Mathematics Excursion Of Mathematics [/et_pb_accordion_item][/et_pb_accordion][et_pb_text _builder_version=”4.0.9″ text_font=”Raleway|300|||||||” text_text_color=”#ffffff” header_font=”Raleway|300|||||||” header_text_color=”#e2e2e2″ background_color=”#0c71c3″ custom_margin=”48px||48px” custom_padding=”20px|20px|0px|20px||” border_radii=”on|5px|5px|5px|5px” box_shadow_style=”preset3″]
Start with hints
[/et_pb_text][et_pb_tabs _builder_version=”4.1″][et_pb_tab title=”HINT 0″ _builder_version=”4.0.9″]Do you really need a hint? Try it first![/et_pb_tab][et_pb_tab title=”HINT 1″ _builder_version=”4.1″ hover_enabled=”0″]First of all look at the examples , see that for all positive , we have.Now what we have to do with this ?
[/et_pb_tab][et_pb_tab title=”HINT 2″ _builder_version=”4.0.9″]Now we have to find which member has what uniform numbers from the given conversation .[/et_pb_tab][et_pb_tab title=”HINT 3″ _builder_version=”4.1″ hover_enabled=”0″]After some simple manipulations , we have . Thus now the problem reduces to finding a value of such that is a perfect square. [/et_pb_tab][et_pb_tab title=”HINT 4″ _builder_version=”4.1″ hover_enabled=”0″]Since is a perfect square, we must also have be a perfect square. In order for to be a perfect square, must be twice a perfect square.[/et_pb_tab][et_pb_tab title=”HINT 5″ _builder_version=”4.1″]
Now check the options and see for what value of n , must be twice a perfect square. works, thus, and our desired answer is [/et_pb_tab][/et_pb_tabs][et_pb_text _builder_version=”3.27.4″ text_font=”Raleway|300|||||||” text_text_color=”#ffffff” header_font=”Raleway|300|||||||” header_text_color=”#e2e2e2″ background_color=”#0c71c3″ min_height=”12px” custom_margin=”50px||50px” custom_padding=”20px|20px|20px|20px” border_radii=”on|5px|5px|5px|5px” box_shadow_style=”preset3″]
Cheenta AMC Training Camp consists of live group and one on one classes, 24/7 doubt clearing and continuous problem solving streams.[/et_pb_blurb][et_pb_button button_url=”https://www.cheenta.com/amc-8-american-mathematics-competition/” url_new_window=”on” button_text=”Learn More” button_alignment=”center” _builder_version=”4.0.9″ custom_button=”on” button_bg_color=”#0c71c3″ button_border_color=”#0c71c3″ button_border_radius=”0px” button_font=”Raleway||||||||” button_icon=”%%3%%” background_layout=”dark” button_text_shadow_style=”preset1″ box_shadow_style=”preset1″ box_shadow_color=”#0c71c3″][/et_pb_button][et_pb_text _builder_version=”3.27.4″ text_font=”Raleway|300|||||||” text_text_color=”#ffffff” header_font=”Raleway|300|||||||” header_text_color=”#e2e2e2″ background_color=”#0c71c3″ custom_margin=”50px||50px” custom_padding=”20px|20px|20px|20px” border_radii=”on|5px|5px|5px|5px” box_shadow_style=”preset3″]