| Prove that root 3 + root 7 is irrational | Prove that √3 + √7 is irrational |

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in this video, I use the method of contradiction to prove that root 3+ root 7 is an irrational number. in this method first, we assume that the given irrational number is a rational number.

let root 3 + root 7 is a rational number so we can write this in the form of p/q where p and q are integers such they do not have any common factor other than one .like 5,7 to 10, 13. this type of numbers is called coprime.

now root 3 + root 7 = p/q
squaring both side the equation
(root3 + root7)² = (root3)² + (root7)² + 2 * (root3) * (root 7) = p/q
= 3 + 7 +2root 21 = p/q
= 10 + 2root 21 = p/q
now transferring the 8 on other side
2 root 21 = p/q - 10
dividing 2 with both side
root 21 = p/2q -10/2 = p/2q-5 or (p-10q)/5

p and q are integers and rational numbers so (p/2q-5) or (p-10q)/5 is also rational number because both are equal. root 21 is also a rational number because they are equal.
but root 21 is an irrational number. this contradicts our prior assumptions.
hence it is proved that root 3+ root 7 is an irrational number.
● Exercise 2.3
● Question 2 (ii) : Prove that √3 + √7 is an irrational number.
● (Topics Covered):
● prove that √3 + √7 is irrational in Hindi
● prove that √3 + √7 is an irrational number
● prove that under root 3 + under root 7 is an irrational number
● prove that √3 + √7 is irrational
● prove that the following are irrational √3 + √7
● prove that the following are irrational under root 3 + under root 7
● prove that root 3 + root 5 is an irrational number
● how to prove irrational numbers class 10
● how to prove irrational numbers class 10 in English
● how to prove irrational numbers class 10 in hindi
● how to prove the irrationality of a number
● how to prove irrational number class 10th

● method of contradiction
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Thank you sir nice explanation immediately I will subscribe your channel

malyadriyadav

Q.2. What is the minimum possible sum of the numbers, if the LCM and the HCF of two numbers are 924 and 7 respectively?

[HOTS

rachnabhatia

Thank your sir ajj mere last board exam hai 🎉

pramilakarra

Sir pls write a vigypan in hindi against black marketing of covid-19 oxygen and medicine. Pls sir 🙏

vikasmahto-vxjo

√21 is rational or irrational number 🇮🇳👳

GAMING_MINU.

Honestly explanation was not good enough 😢

aestheticworld

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