Question

to prove 5+√3 is an irrational number


class10
maths​

Answer 1

Answer:

✅  Hey Mate !  

✅ Here is your answer

• let us assume that 5-√3 is rational number so we can find two integers a , b.

• Where a and b are two co - primes number.

• So it arise contradiction due to our wrong assumption that 5 - √3 is rational number.

• Hence, 5 -√3 is irrational number.

Answer 2

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

❥ Lєt us αssumє , tσ thє cσntrαrч , thαt 5+√3 ís rαtíσnαl.

thαt ís , wє cαn fínd cσprímє α αnd в ( в ≠ 0 ) such thαt 5 + √3 = α/b.

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Thєrєfσrє ,

√3 = $\frac{a}{b}$ - $\frac{5}{1}$

√3 = $\frac{a - 5b}{b}$

❥ But thís cσntrαdícts thє fαct thαt √3 ís írrαtíσnαl.

thís cσntrαdíctíσn hαs αrísєn вєcαusє íf σur íncσrrєct

αssumptíσn thαt 5+√3 ís rαtíσnαl.

Sσ , Wє cσncludє thαt 5+√3 ís írrαtíσnαl.

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$\Large{\underline{\underline{\bf{Additional Information:-}}}}$

❃ What is Rational Number ?

❥ A rαtíσnαl numвєr ís α numвєr thαt cαn вє єхprєss αs thє rαtíσ σf twσ íntєgєrs. α numвєr thαt cαnnσt вє єхprєssєd thαt wαч ís írrαtíσnαl.

❃ What is Irrational Number ?

❥ Thє írrαtíσnαl numвєrs αrє αll thє rєαl numвєrs whích αrє nσt rαtíσnαl numвєrs. thαt ís, írrαtíσnαl numвєrs cαnnσt вє єхprєssєd αs thє rαtíσ σf twσ íntєgєrs. ... ín thє cαsє σf írrαtíσnαl numвєrs, thє dєcímαl єхpαnsíσn dσєs nσt tєrmínαtє, nσr єnd wíth α rєpєαtíng sєquєncє.