whether 2under root 45/ 2 underoot 5 + 3 underroot 20 / 2 underoot 5 on simplification gives a rational or an irrational number

Asked by rusuishika | 16th Jan, 2021, 11:04: PM

Expert Answer:

begin mathsize 16px style fraction numerator 2 square root of 45 over denominator 2 square root of 5 end fraction plus fraction numerator 3 square root of 20 over denominator 2 square root of 5 end fraction
equals fraction numerator 2 square root of 9 cross times 5 end root over denominator 2 square root of 5 end fraction plus fraction numerator 3 square root of 4 cross times 5 end root over denominator 2 square root of 5 end fraction
equals fraction numerator 2 cross times 3 square root of 5 over denominator 2 square root of 5 end fraction plus fraction numerator 3 cross times 2 square root of 5 over denominator 2 square root of 5 end fraction
equals fraction numerator 6 square root of 5 plus 6 square root of 5 over denominator 2 square root of 5 end fraction
equals fraction numerator 12 square root of 5 over denominator 2 square root of 5 end fraction
equals 6
So comma space fraction numerator 2 square root of 45 over denominator 2 square root of 5 end fraction plus fraction numerator 3 square root of 20 over denominator 2 square root of 5 end fraction space on space simplification space gives space straight a space rational space number.
end style

Answered by Yasmeen Khan | 18th Jan, 2021, 01:48: PM