Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 9 Answered

Prove square root of 2 space end root space plus space square root of 5  is a irrational number.
Asked by agraharianiruddha | 20 Jul, 2018, 09:29: PM
answered-by-expert Expert Answer
begin mathsize 16px style Let space square root of 2 space plus space square root of 5 space be space straight a space rational space number. rightwards double arrow square root of 2 space plus space square root of 5 space equals space straight p over straight q rightwards double arrow straight p over straight q space minus space square root of 2 space space equals square root of 5 rightwards double arrow open parentheses straight p over straight q space minus space square root of 2 close parentheses squared space equals space 5 rightwards double arrow straight p squared over straight q squared space minus space fraction numerator 2 space square root of 2 over denominator straight q end fraction straight p space plus space 2 space equals space 5 rightwards double arrow straight p squared over straight q squared space minus space 2 space equals space fraction numerator 2 space square root of 2 over denominator straight q end fraction straight p space rightwards double arrow fraction numerator straight p squared space minus space 2 straight q squared over denominator straight q squared end fraction space equals space fraction numerator 2 straight p over denominator straight q end fraction space square root of 2 rightwards double arrow fraction numerator straight p squared space minus space 2 straight q squared over denominator 2 pq end fraction space equals square root of 2 rightwards double arrow square root of 2 space is space straight a space rationla space number. left parenthesis space since comma space straight p. space straight q space are space integers space rightwards double arrow fraction numerator straight p squared space minus space 2 straight q squared over denominator 2 pq end fraction space is space straight a space rational space numbers right parenthesis But space thist space contradicts space the space fact space that space square root of 2 space is space an space irrational space number. So comma space our space assumption space is space wrong. Hence space square root of 2 space plus space square root of 5 space space is space an space irrational space number. end style
Answered by Yasmeen Khan | 23 Jul, 2018, 11:41: AM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 9 - Maths
laxman saves 10% More than his expenditure and bhuwan spends 10% more than his savings if laxman savings is 10% more than bhuwan expenditure what is the ratio of incomes of laxman and bhuwa
Asked by rathorgaurav2945 | 21 Apr, 2024, 10:31: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
13. If x = (2 + sqrt(3)) find the value of x ^ 2 + 1/(x ^ 2)
Asked by monika.vns14 | 18 Apr, 2024, 05:15: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
3√5+√3/√5-√3
Asked by gulshanelectronics2017 | 15 Apr, 2024, 05:35: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
find the value of n in 7^2n+1÷49=7^3
Asked by tripura78839 | 12 Apr, 2024, 09:05: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
how to solve it
question image
Asked by singhanjali0199 | 12 Apr, 2024, 08:29: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
√2x^2+3x+√2
question image
Asked by killerstealer593 | 11 Apr, 2024, 07:50: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
x²-22x+120
Asked by rson0295 | 01 Apr, 2024, 08:55: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Draw the graph of the equation of line 2x + 3y = 6. Write the co ordinates of the point where the line intersects X-axis and Y-axis.
question image
Asked by saee.shinde3069 | 31 Mar, 2024, 10:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
locate √2 on number line
Asked by rathoreraj7296 | 31 Mar, 2024, 08:09: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
ab is diameter of circle with centre o . CD is a code equal to the radius of the circle a c and b b when extend intersect at the point e prove that angle a e b is equals to 60 degree
Asked by divyanshibirla037 | 29 Mar, 2024, 03:26: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×