{"id":30851,"date":"2023-06-21T13:30:33","date_gmt":"2023-06-21T13:30:33","guid":{"rendered":"https:\/\/moonpreneur.com\/math-corner\/?p=30851"},"modified":"2025-02-08T17:15:36","modified_gmt":"2025-02-08T17:15:36","slug":"vedic-math-ekadhikena-purvena","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/vedic-math-ekadhikena-purvena\/","title":{"rendered":"Vedic Math Sutra: Sutra 1- Ekadhikena Purvena"},"content":{"rendered":"\t\t
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Update:<\/strong> This article was last updated on 6th February 2025 to reflect the accuracy and up-to-date information on the page.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Introducing our new series on <\/span>Vedic Mathematics<\/span><\/a>: “<\/span>Unveiling the 16 Sutras<\/span>“.<\/span> This<\/span> ancient system of mathematics<\/span>,<\/span> developed<\/span> in ancient India, provides <\/span>several techniques and sutras (formulas) for<\/span> doing<\/span> calculations <\/span>fast and efficiently.<\/span>
<\/span>
<\/span>Recommended Reading: <\/b><\/span>Vedic Math Sutras: Sutra 2-Nikhilam Navatashcaramam Dashatah\u00a0<\/span><\/a><\/p>

In this educational journey, we are<\/span> going<\/span> to<\/span> uncover the ancient techniques, and we are starting<\/span> with the <\/span>mighty sutra called Ekadhikena Purvena, a shortcut to square.<\/span><\/span><\/p>

Translated as \u201cby one more than the previous,\u201d this sutra is the foundation for <\/span>mental<\/span><\/a> calculations and is the key to unlocking mathematical prowess.\u00a0<\/span><\/p>

Ekadhikena Purvena<\/span>‘s<\/span> power<\/span> is<\/span> the<\/span> acceleration<\/span> of<\/span> computation, making it highly useful to astronomers and engineers in ancient India. The concept was very<\/span> handy in astronomical calculations, where exact<\/span> and <\/span>rapid<\/span> calculations<\/span> were <\/span>required<\/span> for<\/span> tracking<\/span> planetary positions, <\/span>predicting<\/span> eclipses, and <\/span>determining celestial alignments.<\/span><\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Ekadhikena Purvena in Engineering and Modern Applications<\/b><\/span><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Indian mathematicians such as Brahmagupta and Bhaskara II applied<\/span> the<\/span> same<\/span> methodology<\/span> as <\/span>Ekadhikena Purvena to solve algebra and <\/span>geometric problems<\/span>. The sutra has <\/span>been<\/span> effective<\/span> enough<\/span> to<\/span> remain<\/span> valuable <\/span>in <\/span>the<\/span> present<\/span> too in various disciplines like:<\/span>
<\/span>\u2705 <\/span>Computer algorithms<\/b> \u2013 Quick<\/span> computation<\/span> in <\/span>logic of <\/span>programming<\/span>
<\/span>\u2705 <\/span>Astronomical modeling<\/b> \u2013 Rapid<\/span> estimation <\/span>techniques<\/span> for <\/span>tracking <\/span>celestial <\/span>bodies<\/span>
<\/span>\u2705 <\/span>Engineering calculations<\/b> \u2013 Quick<\/span> multiplication <\/span>techniques<\/span> of<\/span> the laws of <\/span>physics and <\/span>building formulas<\/span><\/span><\/p>

Despite being an ancient technique, Ekadhikena Purvena remains highly applicable in modern mathematics and competitive exams. Its efficiency proves how timeless Vedic Math techniques are, making them valuable for students as well as professionals.<\/span><\/p>

This <\/span>is a <\/span>versatile technique<\/span>,<\/span> with<\/span> easy <\/span>multiplication when the <\/span>two numbers have a <\/span>unit digit sum of <\/span>10.<\/span><\/span><\/p>

Steps<\/strong><\/span><\/h3>

Here is the step-by-step process of applying the Ekadhikena Purvena sutra:<\/span><\/p>

\u201cEkadhikena Purvena\u201d is a sutra (formula) in Vedic mathematics, which means \u201cBy one more than the previous one.\u201d This sutra is used to square numbers close to a power of 10, typically when the number\u2019s last digit(s) is(are) small.<\/span><\/p>

But 45 is far from a power of 10. If we apply the sutra directly, the calculations are pretty complicated.<\/span><\/p>

However, if you still want to use the Ekadhikena Purvena method, you can use the nearest base of 50, which is more convenient.<\/span><\/p>

1. Let\u2019s apply the Ekadhikena Purvena sutra to find the square of 45.<\/span><\/p>

First, split the number into two parts: the part that doesn\u2019t include the 5 (4 in this case) and the 5.<\/span><\/p>

A: 4<\/span><\/p>

B: 5<\/span><\/p>

2. Now, take the part of the number that doesn\u2019t include the 5 (4) and add 1, making it 5.<\/span><\/p>

C: 4+1=5<\/span><\/p>

3. Multiply the original number that doesn\u2019t include the 5 (4) by the number you just calculated (5). This gives you 20.<\/span><\/p>

AXC<\/span><\/p>

4\u00d75= 20<\/span><\/p>

4. Then append 25 (the square of 5) to the result from step 3.\u00a0<\/span><\/p>

So, the result is 2025<\/span><\/p>

The next one will be Nikhilam Navatashcaraman Dashatah.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Common Mistakes & Tips for Using Ekadhikena Purvena<\/b><\/span><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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While <\/span>Ekadhikena Purvena<\/b> is a powerful mental math technique, beginners often make mistakes when applying the sutra. Here are some <\/span>common errors<\/b> and <\/span>tips<\/b> to avoid them:<\/span><\/span><\/p>

Common Mistakes<\/b><\/span><\/h4>

1. Forgetting to add one<\/b> \u2013 The core idea of <\/span>Ekadhikena Purvena<\/b> is to add <\/span>one more than the previous number<\/b>. Missing this step leads to incorrect calculations.<\/span><\/span><\/p>

2. Misplacing digits while appending 25<\/b> \u2013 The second part of the answer (25) should always be placed at the end. Some students mistakenly place it in the middle.<\/span><\/span><\/p>

3. Applying it to incorrect numbers<\/b> \u2013 This sutra works best for numbers ending in 5. Applying it to other numbers directly can cause confusion.<\/span><\/span><\/p>

4. Skipping mental verification<\/b> \u2013 Although<\/span> Ekadhikena Purvena <\/span>accelerates<\/span> the<\/span> calculations, it <\/span>is <\/span>always <\/span>advisable<\/span> to quickly <\/span>check<\/span> the <\/span>results <\/span>in order <\/span>to avoid <\/span>mistakes<\/span>.<\/span><\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Quick Tips for Rapid and Accurate Calculations<\/b><\/span><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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\u2705 <\/span>Practice with simple numbers first<\/b> \u2013 Before trying<\/span> the larger numbers, try Ekadhikena Purvena with smaller values such<\/span> as 15\u00b2, 25\u00b2, and 35\u00b2.<\/span>
<\/span>\u2705 <\/span>Understand the logic behind the sutra<\/b> \u2013 Knowing that <\/span>Ekadhikena Purvena<\/b> means “one more than the previous” helps in grasping the concept better.<\/span>
<\/span>\u2705 <\/span>Write intermediate steps if needed<\/b> \u2013 Until you master the sutra, jot down calculations to reinforce accuracy.<\/span>
<\/span>\u2705 <\/span>Use visualization techniques<\/b> \u2013 Picture the steps in your mind for faster recall.<\/span><\/span><\/p>

Mastering Ekadhikena Purvena not only develops<\/span> the<\/span> ability<\/span> to mentally calculate rapidly <\/span>but also <\/span>instills<\/span> confidence in <\/span>mental <\/span>handling <\/span>of <\/span>complex math problems. <\/span>Continue<\/span> practicing, and soon<\/span> squaring numbers mentally will become second nature!<\/span><\/span><\/p>

Moonpreneur understands the requirements and demands this rapidly changing technological world is bringing with it for our children. Our expert-designed <\/span>Advanced Math course<\/span><\/a> for 3rd, 4th, 5th, and 6th will teach<\/span> your child math hands-on, excite <\/span>him<\/span> to learn and <\/span>make<\/span> it<\/span> possible<\/span> to implement <\/span>real<\/span> <\/span>life.<\/span> Register <\/span><\/span>now for a free <\/span>60-minute Advanced Math Workshop<\/span><\/a>.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\n\t\t\t\t\t\t\t\t\t\t\t\t\"16\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

Update: This article was last updated on 6th February 2025 to reflect the accuracy and up-to-date information on the page. Introducing our new series on Vedic Mathematics: “Unveiling the 16 Sutras”. This ancient system of mathematics, developed in ancient India, provides several techniques and sutras (formulas) for doing calculations fast and efficiently. Recommended Reading: Vedic […]<\/p>\n","protected":false},"author":21,"featured_media":30854,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[979,980,981,982,983,978],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/30851"}],"collection":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/users\/21"}],"replies":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/comments?post=30851"}],"version-history":[{"count":17,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/30851\/revisions"}],"predecessor-version":[{"id":34894,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/30851\/revisions\/34894"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media\/30854"}],"wp:attachment":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media?parent=30851"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/categories?post=30851"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/tags?post=30851"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}