{"id":39053,"date":"2025-06-26T18:19:05","date_gmt":"2025-06-26T18:19:05","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=39053"},"modified":"2025-06-26T18:19:06","modified_gmt":"2025-06-26T18:19:06","slug":"which-among-the-following-is-a-perfect-square","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-among-the-following-is-a-perfect-square\/","title":{"rendered":"Which among the following is a perfect square"},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">Which among the following is a perfect square<\/pre>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"376\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-377-1024x376.png\" alt=\"\" class=\"wp-image-39054\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-377-1024x376.png 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-377-300x110.png 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-377-768x282.png 768w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-377-1536x564.png 1536w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-377.png 2037w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is <strong>(B) 323761<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>A <em>perfect square<\/em> is a number that results from squaring a whole number. To determine whether a number is a perfect square, we can begin by estimating its square root and then checking whether the square of that root gives the original number. Alternatively, we can apply divisibility rules and digital root techniques to eliminate candidates quickly before verifying with exact calculations.<\/p>\n\n\n\n<p>Let\u2019s examine 323761:<\/p>\n\n\n\n<p>The square root of 323761 is approximately 569. Calculating directly:<\/p>\n\n\n\n<p>5692=569\u00d7569=(500+69)2=5002+2\u00d7500\u00d769+692=250000+69000+4761=323761569^2 = 569 \\times 569 = (500 + 69)^2 = 500^2 + 2 \\times 500 \\times 69 + 69^2 = 250000 + 69000 + 4761 = 323761<\/p>\n\n\n\n<p>This confirms that 323761 is indeed a perfect square because it is the square of the integer 569.<\/p>\n\n\n\n<p>Now, consider the digital root method. If a number is a perfect square, its digital root must be 1, 4, 7, or 9.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>323761 \u2192 3+2+3+7+6+1 = 22 \u2192 2+2 = 4, which is acceptable for a perfect square.<\/li>\n\n\n\n<li>For comparison:\n<ul class=\"wp-block-list\">\n<li>455562 \u2192 digits sum to 27 \u2192 2+7 = 9 (possible but needs checking)<\/li>\n\n\n\n<li>675487 \u2192 digits sum to 37 \u2192 3+7 = 10 \u2192 1+0 = 1 (possible)<\/li>\n\n\n\n<li>897568 \u2192 digits sum to 43 \u2192 4+3 = 7 (possible)<\/li>\n\n\n\n<li>347860 \u2192 digits sum to 28 \u2192 2+8 = 10 \u2192 1+0 = 1 (possible)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>While many options have valid digital roots, only <strong>323761 produces an integer when square-rooted exactly<\/strong>. All others result in non-integer values.<\/p>\n\n\n\n<p>Hence, 323761 is a perfect square and the correct choice.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1115.jpeg\" alt=\"\" class=\"wp-image-39055\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1115.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1115-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1115-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which among the following is a perfect square The Correct Answer and Explanation is: The correct answer is (B) 323761. Explanation: A perfect square is a number that results from squaring a whole number. To determine whether a number is a perfect square, we can begin by estimating its square root and then checking whether [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-39053","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39053","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=39053"}],"version-history":[{"count":2,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39053\/revisions"}],"predecessor-version":[{"id":39057,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39053\/revisions\/39057"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=39053"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=39053"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=39053"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}