Q. 7

# Using (√7 + √3)(√7 — √3) = 4 and the fact that (√7 + √3) is irrational prove that √7 — √3 is irrational.

Given ( + )() = 4 and ( + ) is irrational.

(multiplying numerator and denominator by )

=

(we know that (a – b) × (a + b) = (a2 – b2))

= =

Here, it is given that is irrational and we know that 4 is rational.

Therefore,

We know that rational divided by irrational is always irrational.

So, is irrational.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz:Euclid's Division Lemma44 mins
Fundamental Theorem of Arithmetic-238 mins
Champ Quiz | Fundamental Principle Of Arithmetic41 mins
Fundamental Theorem of Arithmetic- 143 mins
NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Euclids Division Lemma49 mins
Quiz | Imp Qs on Real Numbers37 mins
Interactive Quiz - HCF and LCM32 mins
Application of Euclids Division Lemma50 mins
Relation Between LCM , HCF and Numbers46 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Prove is irrational.

Gujarat Board Mathematics

√4 + 3 is……..

Gujarat Board Mathematics

Simplify :

Gujarat Board Mathematics

Simplify :

Gujarat Board Mathematics