{"id":31005,"date":"2023-06-28T13:29:33","date_gmt":"2023-06-28T13:29:33","guid":{"rendered":"https:\/\/moonpreneur.com\/math-corner\/?p=31005"},"modified":"2025-01-08T09:43:24","modified_gmt":"2025-01-08T09:43:24","slug":"puranapuranabhyam","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/puranapuranabhyam\/","title":{"rendered":"Vedic Math Sutra: Sutra 8 -Puranapuranabhyam"},"content":{"rendered":"\t\t
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Update:<\/strong> This article was last updated on 8th January 2025<\/span><\/strong> to reflect the accuracy and up-to-date information on the page.<\/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\"Vedic\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
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Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.<\/em>
\u2014 Richard Courant, German-American mathematician<\/strong><\/em><\/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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The Vedic Math Sutra 8 is known as Puranapuranabhyam, which literally means \u2013 By the completion or non-completion. This sutra can be used to do the calculations based on complements or non-complements of numbers. The Vedic Maths workbooks for Level 8 are a great source of mastering advanced mathematical concepts with ease and efficiency. Let’s learn how this sutra can be applied.<\/p>

Recommended Reading:<\/b> VEDIC MATH SUTRA: SUTRA 3 \u2013 URDHAVA \u2013 TIRYAGBYHAM<\/span><\/a><\/p>

This sutra can be applied to factorize and solve quadratic and cubic & bi-quadratic equations. This is how this sutra can be effectively used in factorizing and solving quadratic, cubic, and bi-quadratic equations in the Vedic Maths book for class 8.<\/span><\/p>

The Sutra States<\/span><\/h4>

\u201c<\/span>Puranapuranabhyam<\/b>\u201d (By the completion or non-completion) \u2013 \u201cWhatever is to be added to the completed (Purana) or non-completed (Apurna) in one is added to the other.\u201d<\/span><\/p>

Image:<\/p>

To grasp this puranapuranabhyam, sutra better, let’s take an example.<\/span><\/p>

Example 1<\/b><\/h4>

Solve the quadratic equation 2x^2 + 5x – 3 = 0 using Vedic Mathematics.<\/span><\/p>

Step 1: <\/b>Understand the Quadratic Equation<\/span><\/p>

The given quadratic equation is 2x^2 + 5x – 3 = 0.<\/span><\/p>

Step 2: <\/b>Identify the Values<\/span><\/p>

From the equation, we can identify the values as follows:<\/span><\/p>

a = 2<\/span><\/p>

b = 5<\/span><\/p>

c = -3<\/span><\/p>

Step 3: <\/b>Apply the Puranapuranabhyam Sutra<\/span><\/p>

The product of the sum and difference of two numbers is equal to the difference of their squares.<\/span><\/p>

Let\u2019s find two numbers whose product equals ac, which is 2*(-3) = -6, and whose sum is equal to b, which is 5.<\/span><\/p>

Let\u2019s say m and n are those two numbers.<\/span><\/p>

Step 4: <\/b>Factorize the Quadratic Equation<\/span><\/p>

We need to find two numbers whose product is -6 and whose sum is 5.<\/span><\/p>

By inspection, we can see that 6 and -1 fit these conditions since 6 * (-1) = -6 and 6 + (-1) = 5.<\/span><\/p>

Therefore, we can rewrite the quadratic equation as follows:<\/span><\/p>

2x^2 + 6x – x – 3 = 0<\/span><\/p>

Now, we can factorize it by grouping<\/span><\/p>

2x(x + 3) – 1(x + 3) = 0<\/span><\/p>

Notice that we have a common factor of (x + 3). Factoring it out, we get:<\/span><\/p>

(x + 3)(2x – 1) = 0<\/span><\/p>

Step 5: <\/b>Solve for x<\/span><\/p>

Now, we’ll set each factor equal to zero and solve for x:<\/span><\/p>

x + 3 = 0 –> x = -3<\/span><\/p>

2x – 1 = 0 –> 2x = 1 –> x = \u00bd<\/span><\/p>

These are the two roots of the quadratic equation 2x^2 + 5x – 3 = 0, obtained using Vedic Mathematics.<\/span><\/p>

Therefore, the roots are x = -3 and x = 1\/2.<\/span><\/p>

You can check these roots by putting them back in the original equation.<\/span><\/p>

The Puranapuranabhyam sutra of Vedic Maths is one of the most important concepts for students of 8th class, and it may help to do the calculations more easily using complements and non-complements. However, one has to practice and be familiar with the different uses of Vedic Math sutras<\/a>.<\/span><\/p>

Recommended reading: Vedic Math Sutra: Sutra-15 Gunitasamuccayah<\/a><\/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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Recommended Reading: <\/b>HOW VEDIC MATH CAN HELP GEN Z TO OVERCOME MATH FEAR<\/span><\/a><\/p>

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Sign-up for a free<\/span> 60-minute Advanced Math Workshop <\/span><\/a>today!<\/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\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 8th January 2025 to reflect the accuracy and up-to-date information on the page. Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.\u2014 Richard […]<\/p>\n","protected":false},"author":116,"featured_media":31007,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[980,981,982,983,978],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/31005"}],"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\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/comments?post=31005"}],"version-history":[{"count":19,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/31005\/revisions"}],"predecessor-version":[{"id":34587,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/31005\/revisions\/34587"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media\/31007"}],"wp:attachment":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media?parent=31005"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/categories?post=31005"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/tags?post=31005"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}