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Rational and Irrational Numbers | Rational and Irrational Numbers Exercise 1.5

Question 2

. Simplify:

(i) (7 + 3√5) / (7 - 3√5)

(ii) (3 - 2√2) / (3 + 2√2)

(iii) (5 - 3√14) / (7 + 2√14)

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  • Solution

  • Transcript

(i) (7 + 3√5) / (7 - 3√5)

Let us rationalize the denominator, we get

(7 + 3√5) / (7 - 3√5) = [(7 + 3√5) (7 + 3√5)] / [(7 - 3√5) (7 + 3√5)]

(ii) (3 - 2√2) / (3 + 2√2)

Let us rationalize the denominator, we get

(3 - 2√2) / (3 + 2√2) = [(3 - 2√2) (3 - 2√2)] / [(3 + 2√2) (3 - 2√2)]

(iii) (5 - 3√14) / (7 + 2√14)

Let us rationalize the denominator, we get

(5 - 3√14) / (7 + 2√14) = [(5 - 3√14) (7 - 2√14)] / [(7 + 2√14) (7 - 2√14)]

"hey guys welcome to lido q a video i'm vinit your lido tutor and i'm bringing this question on your screen simplify and we have these three questions so we are going to take a look at them one by one the first one is 7 plus 3 root 5 by 7 minus 3 root 5 so we are just going to rationalize the denominator to rationalize the denominator we multiply by the inverse so if it is minus 7 by 7 minus 3 by 5 we multiply by 7 plus 3 by 5 remember this is the formula we always use when we rationalize the denominator right we try to bring the denominator in this form and we get a whole number so 7 plus 3 root 5 so this will be equal to 7 plus 3 root 5 whole square by 7 square minus 3 root 5 square so this will be 7 square is equal to 49 so a square plus 2 a b plus b square plus 42 root 5 plus 3 root 5 whole square is 45 right yeah by 49 minus 45 so this is equal to 94 plus 42 root 5 by 4 or equal to we can take 2 common 47 plus 21 root 5 by 4 so this is equal to 47 plus 21 root 5 by 2 wasn't that easy guys i think it was let us look at number 2 3 minus 2 root 2 by 3 plus 2 root 2 again we rationalize the denominator by factorizing it 3 minus 2 root 2 so we get 3 minus 2 root 2 whole square by 3 minus 3 square minus 2 root 2 whole square this is equal to 9 minus 12 root 2 plus 8 by 9 minus 8 so this is equal to 17 minus 12 root 2 isn't that easy very easy guys now let us look at third one so we don't have a space here so we are going to do the third one on this left space okay so let us look at number 3 5 minus 3 root 14 by 7 plus 2 root 14 again factorizing or rationalizing the denominator we get this now we multiply so 5 minus 3 root 14 into 7 minus 2 root 14 by 7 square minus 2 root 14 whole square so this is equal to 35 minus 10 root 14 minus 21 root 14 plus 14 into 6 is 84 yeah 3 to the 6 and 14 square root 14 square is 14 by 49 minus 14 into 4 is equal to 56 so this is equal to 35 plus 84 will be equal to 119 minus uh sorry my seven threes are 21 and then we have five yeah minus 31 root 14 by minus 7 this is our answer so that was easy guys if you still have a doubt please leave a comment below do like our video and subscribe to our channel i'll see you in our next video until then bye guys keep practicing"

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Question 2

. Simplify:

(i) (7 + 3√5) / (7 - 3√5)

(ii) (3 - 2√2) / (3 + 2√2)

(iii) (5 - 3√14) / (7 + 2√14)

  • Solution

  • Transcript

(i) (7 + 3√5) / (7 - 3√5)

Let us rationalize the denominator, we get

(7 + 3√5) / (7 - 3√5) = [(7 + 3√5) (7 + 3√5)] / [(7 - 3√5) (7 + 3√5)]

(ii) (3 - 2√2) / (3 + 2√2)

Let us rationalize the denominator, we get

(3 - 2√2) / (3 + 2√2) = [(3 - 2√2) (3 - 2√2)] / [(3 + 2√2) (3 - 2√2)]

(iii) (5 - 3√14) / (7 + 2√14)

Let us rationalize the denominator, we get

(5 - 3√14) / (7 + 2√14) = [(5 - 3√14) (7 - 2√14)] / [(7 + 2√14) (7 - 2√14)]

"hey guys welcome to lido q a video i'm vinit your lido tutor and i'm bringing this question on your screen simplify and we have these three questions so we are going to take a look at them one by one the first one is 7 plus 3 root 5 by 7 minus 3 root 5 so we are just going to rationalize the denominator to rationalize the denominator we multiply by the inverse so if it is minus 7 by 7 minus 3 by 5 we multiply by 7 plus 3 by 5 remember this is the formula we always use when we rationalize the denominator right we try to bring the denominator in this form and we get a whole number so 7 plus 3 root 5 so this will be equal to 7 plus 3 root 5 whole square by 7 square minus 3 root 5 square so this will be 7 square is equal to 49 so a square plus 2 a b plus b square plus 42 root 5 plus 3 root 5 whole square is 45 right yeah by 49 minus 45 so this is equal to 94 plus 42 root 5 by 4 or equal to we can take 2 common 47 plus 21 root 5 by 4 so this is equal to 47 plus 21 root 5 by 2 wasn't that easy guys i think it was let us look at number 2 3 minus 2 root 2 by 3 plus 2 root 2 again we rationalize the denominator by factorizing it 3 minus 2 root 2 so we get 3 minus 2 root 2 whole square by 3 minus 3 square minus 2 root 2 whole square this is equal to 9 minus 12 root 2 plus 8 by 9 minus 8 so this is equal to 17 minus 12 root 2 isn't that easy very easy guys now let us look at third one so we don't have a space here so we are going to do the third one on this left space okay so let us look at number 3 5 minus 3 root 14 by 7 plus 2 root 14 again factorizing or rationalizing the denominator we get this now we multiply so 5 minus 3 root 14 into 7 minus 2 root 14 by 7 square minus 2 root 14 whole square so this is equal to 35 minus 10 root 14 minus 21 root 14 plus 14 into 6 is 84 yeah 3 to the 6 and 14 square root 14 square is 14 by 49 minus 14 into 4 is equal to 56 so this is equal to 35 plus 84 will be equal to 119 minus uh sorry my seven threes are 21 and then we have five yeah minus 31 root 14 by minus 7 this is our answer so that was easy guys if you still have a doubt please leave a comment below do like our video and subscribe to our channel i'll see you in our next video until then bye guys keep practicing"

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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