{"id":233289,"date":"2025-06-13T03:54:06","date_gmt":"2025-06-13T03:54:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233289"},"modified":"2025-06-13T03:54:10","modified_gmt":"2025-06-13T03:54:10","slug":"between-what-two-consecutive-integers-does-the-square-root-of-205-lie","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/between-what-two-consecutive-integers-does-the-square-root-of-205-lie\/","title":{"rendered":"Between what two consecutive integers does the square root of 205 lie"},"content":{"rendered":"\n

Between what two consecutive integers does the square root of 205 lie? A. 11 & 12 B. 12 & 13 C. 13 & 14 D. 14 & 15 20. Which of the statements is TRUE? A. V is a natural number C. 781 is an irrational number B. 36 is a rational number D. 49 is neither rational nor irrational<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answers:<\/strong><\/p>\n\n\n\n

Question 1:<\/strong>
The square root of 205 lies between 14 and 15.<\/strong>
Answer: D. 14 & 15<\/strong><\/p>\n\n\n\n

Question 2:<\/strong>
Answer: B. 36 is a rational number<\/strong><\/p>\n\n\n\n

\n\n\n\n

Detailed Explanation<\/strong><\/h3>\n\n\n\n

Question 1: Between what two consecutive integers does \u221a205 lie?<\/strong><\/h4>\n\n\n\n

To find between which two integers \u221a205 lies, consider perfect squares close to 205:<\/p>\n\n\n\n

    \n
  • 14\u00b2 = 196<\/li>\n\n\n\n
  • 15\u00b2 = 225<\/li>\n<\/ul>\n\n\n\n

    Now compare:<\/p>\n\n\n\n

      \n
    • \u221a196 = 14<\/li>\n\n\n\n
    • \u221a225 = 15<\/li>\n\n\n\n
    • \u221a205 is between 196 and 225<\/li>\n<\/ul>\n\n\n\n

      Since 196 < 205 < 225, it means:14<205<1514 < \\sqrt{205} < 1514<205\u200b<15<\/p>\n\n\n\n

      Thus, the correct answer is:
      D. 14 & 15<\/strong><\/p>\n\n\n\n

      We can estimate further:<\/p>\n\n\n\n

        \n
      • Try 14.3\u00b2 = 204.49<\/li>\n\n\n\n
      • Try 14.4\u00b2 = 207.36<\/li>\n<\/ul>\n\n\n\n

        So, \u221a205 \u2248 14.3 (which confirms it lies between 14 and 15)<\/p>\n\n\n\n

        \n\n\n\n

        Question 2: Which of the statements is TRUE?<\/strong><\/h4>\n\n\n\n

        Let\u2019s evaluate each choice:<\/p>\n\n\n\n

          \n
        • A. V is a natural number<\/strong>
          This is incomplete or meaningless as “V” is not defined in the question.<\/li>\n\n\n\n
        • B. 36 is a rational number<\/strong>
          A rational number<\/strong> is any number that can be expressed as a fraction a\/b<\/strong> where a<\/strong> and b<\/strong> are integers and b \u2260 0<\/strong>.
          Since 36 = 36\/1<\/strong>, it is a rational number.
          \u2705 This is TRUE.<\/strong><\/li>\n\n\n\n
        • C. 781 is an irrational number<\/strong>
          781 is a whole number and can be written as 781\/1, so it is rational. \u274c False.<\/li>\n\n\n\n
        • D. 49 is neither rational nor irrational<\/strong>
          49 is a whole number (49 = 7\u00b2) and therefore rational<\/strong>. \u274c False.<\/li>\n<\/ul>\n\n\n\n

          Correct answer: B. 36 is a rational number<\/strong><\/p>\n\n\n\n

          \n\n\n\n

          Conclusion<\/strong><\/h3>\n\n\n\n
            \n
          • \u221a205 lies between 14 and 15<\/strong><\/li>\n\n\n\n
          • The true<\/strong> statement is: 36 is a rational number<\/strong><\/li>\n<\/ul>\n\n\n\n
            \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

            Between what two consecutive integers does the square root of 205 lie? A. 11 & 12 B. 12 & 13 C. 13 & 14 D. 14 & 15 20. Which of the statements is TRUE? A. V is a natural number C. 781 is an irrational number B. 36 is a rational number D. 49 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-233289","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233289","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=233289"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233289\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233289"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233289"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233289"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}