CBSE > Class 10 > Mathematics | CBSE Board | Homework Help

We have to prove that √5 is an irrational number It can be proved using the contradiction method Assuming √5 as a rational number, i.e., can be written in the form a/b where a and b are integers with no common factors other than 1 and b is not equal to zero. √5/1 = a/b √5b = a By squaring on both sides (5b)2 = (a)2 b2 = a2/5 …. (1) It means that 5 divides a2. It means that it also divides a a/5 = c a = 5c By squaring on both sides a2 = 25c2 Substituting the value of a2 in equation (1) 5b2 = 25c2 b2 = 5c2 b2/5 = c2 As b2 is divisible by 5, b is also divisible by 5 a and b have a common factor as 5 It contradicts the fact that a and b are coprime This has arisen due to the incorrect assumption as √5 is a rational number. Therefore, √5 is irrational.

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Akeet Deep 9 months ago

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Manu and Aiza are competing in a 60 km/h greater than Manu's average speed and she finished the race in hours less than Manu Find the time taken by Manu to finish the race. Show your work.

Posted by Simba Simba 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Karrii Vijay 9 months ago

3 hrs

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What is The Formula Of (a+b+c)³

Posted by Sahil Kumar 9 months ago

CBSE > Class 10 > Mathematics

4 answers

Nitin Kumar 9 months ago

a³+b³+c³+3(a+b)(b+c)(c+a). Right answer

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Dashrath Singh Sisodiya 9 months ago

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Harinie S 9 months ago

a+b+c+3a²b+3ab²

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Brajmohan Brajmohan 9 months ago

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Two tangents are inclined at an angle of 120° are drawn to circle of radius ‘r'.If length of each tangent is 2√3cm, then ‘r’ is equal to_____

Posted by Himanshi Thakur 9 months ago

CBSE > Class 10 > Mathematics

4 answers

Himanshi Thakur 9 months ago

6 is right answer on SQP but I don't know how to Solve it

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Himanshi Thakur 9 months ago

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Pramith Fernandes A 9 months ago

2 CM IS THE ANSWER

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Pramith Fernandes A 9 months ago

2 CM IS THE ANSWER

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Prove that 5 is irrational.

Posted by Deepanshu Yadav 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Himanshi Thakur 9 months ago

Let √5 be a rational number. then it must be in form of pq where, q≠0 ( p and q are co-prime) √5=pq √5×q=p Suaring on both sides, 5q2=p2 --------------(1) p2 is divisible by 5. So, p is divisible by 5. p=5c Suaring on both sides, p2=25c2 --------------(2) Put p2 in eqn.(1) 5q2=25(c)2 q2=5c2 So, q is divisible by 5. . Thus p and q have a common factor of 5. So, there is a contradiction as per our assumption. We have assumed p and q are co-prime but here they a common factor of 5. The above statement contradicts our assumption. Therefore, √5 is an irrational number.

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The product of two consecutive positive integers is divisible by 2. Is this statement true or false? Give reasons

Posted by Manasvi Bhandari 9 months ago

CBSE > Class 10 > Mathematics

3 answers

Alfiya💫💫💫 . 9 months ago

Yes, it is true as you can check it by taking 1&2 or 3&4 or any other pair 1x2=2. ( divisible by 2) 3x4=12(it is also divisible by 2).. Hence the statement is true. Clear💫💫💫..

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Bhakti Mehta 9 months ago

It is true. Because in any two consecutive positive integers, one will always by divisible by two.For example, 17 and 18 are consecutive numbers;here 18 is divisible by 2 and 17 × 18 equals 306 which is divisible by 2.

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Sai Pansare 9 months ago

No, As in the two consecutive no. One of them is going to be even and the other would odd so the sum a odd no. and a even no. is always odd which is not divisible by 2

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If the a=50,d=-4 and Sn =0 then find n.

Posted by Ayush Kumar 9 months, 1 week ago

CBSE > Class 10 > Mathematics

3 answers

Deepali Vishnoi 9 months ago

The distance between the points (0,2/5)and (-2/5,0)is

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Shuhbham Mahakud 9 months, 1 week ago

Sn = n/2 [2a + (n-1)d] Substituting values :- 0 = n/2 [2(50) + (n-1)(-4)] 0 = n/2 [100 - 4n + 4] 0 = n/2 [104 - 4n] 0 = n/2 × 4 [ 26 - n ] 0 = 2n [ 26 - n ] 0 = 26 - n - 26 = - n 26 = n. This should be the answer according to me.

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Its Vicky 9 months, 1 week ago

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Write down the LCM of the following polynomial: (x-1)(x-2) and (x-2)(x-7)

Posted by Nitin Kumar 9 months, 1 week ago

CBSE > Class 10 > Mathematics

3 answers

Akanksha Kumari 9 months, 1 week ago

(x-1) (x-2) (x-7)

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Stanzin Lhadon 9 months, 1 week ago

(x-2)(x-7)(x-1)

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Aditya Sinha 9 months ago

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Write down the LCM of the following polynomial: (x-2)(x-2) and (x-2)(x-7)

Posted by Nitin Kumar 9 months, 1 week ago

CBSE > Class 10 > Mathematics

3 answers

Sarthak Malviya 9 months ago

LCM will be (x-2)(x-2)(x-7)

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Sarthak Malviya 9 months ago

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Ritika Chauhan 9 months ago

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The pair of equations x=a and y=b graphically represent lines which are

Posted by Tanu Mishra 9 months, 1 week ago

CBSE > Class 10 > Mathematics

1 answers

Raunak Singh 9 months, 1 week ago

Intersecting at point (a,b)

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The longest diameter of a cone can be fully fitted in a cube of edge 8 cm is

Posted by Harini Sree 9 months, 1 week ago

CBSE > Class 10 > Mathematics

2 answers

S. Youthish Kumar 9 months, 1 week ago

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Raunak Singh 9 months, 1 week ago

8 cm of diameter can be fitted with a height of 8 cm

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If a and b are the roots of equation x² - 2 find a³ - b³

Posted by Pau James 9 months, 1 week ago

CBSE > Class 10 > Mathematics

2 answers

Sarthak Malviya 9 months ago

A=-2or2 and b=2or-2 then answer is -16 or 16

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S. Youthish Kumar 9 months, 1 week ago

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If zeros of the polynomial X square + 4 x + 2 are alpha and 2 by Alpha then find the value of a

Posted by Vishnu Adduri 9 months, 1 week ago

CBSE > Class 10 > Mathematics

0 answers

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Sin 30 +tan45/sec30 + cot45

Posted by Siju Divy 9 months, 1 week ago

CBSE > Class 10 > Mathematics

2 answers

Ritika Chauhan 9 months, 1 week ago

Solution - Sin30° = 1/2 , tan 45° = 1 , sec 30° = 2/√3 , cot45° = 1 = 1/2 + 1 ÷ √3/2 + 1 = 1+2 / 2 ÷ √3 + 2 / 2 = 3 / 2 × 2 / √3 + 2 = 3 / √3 + 2 = √3 × √3 / √3 + 2 = √3 / 2 = Sin 60° answer I hope this is helpful to you...~

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Kavya Rajvanshi 9 months, 1 week ago

1/2+1÷ 2/√3+1 = 1+2/3 ÷ 2+√3/2√3 = 3√3(2-√3)/2 is a answer

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the diagram shows a grid of number squares a small marble is placed in first square a fair die is thrown if 145 or 6 turns up then marble is moved one square to the right if two or three turns up then marble is moved

Posted by Vaishali Limanpure 9 months, 1 week ago

CBSE > Class 10 > Mathematics

0 answers

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Find the ratio in which the line segment joining the points (-3,10) and (6,-8)is divided by (-1,6)

Posted by Parimal Katpatal 9 months, 1 week ago

CBSE > Class 10 > Mathematics

3 answers

Sai Pansare 9 months ago

Let the ratio in which the line segment joining A(- 3, 10) and B(6, - 8) be divided by point C(- 1, 6) be k : 1. By Section formula, C(x, y) = [(mx₂ + nx₁) / m + n, (my₂ + ny₁) / m + n] m = k, n = 1 Therefore, - 1 = (6k - 3) / (k + 1) - k - 1 = 6k - 3 7k = 2 k = 2 / 7 Hence, the point C divides line segment AB in the ratio 2 : 7.

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Raunak Singh 9 months, 1 week ago

2:7

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Parimal Katpatal 9 months, 1 week ago

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In the adjoining figure, DE||BC .The value of X is

Posted by Sushmita Chauhan 9 months, 1 week ago

CBSE > Class 10 > Mathematics

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1+tan²A /1+cot²A=sec²-1 prove

Posted by 👿 B Basava 😈 9 months, 1 week ago

CBSE > Class 10 > Mathematics

2 answers

Shuhbham Mahakud 9 months ago

TO PROVE:-(1+tan²A)/(1+cot²A) = sec²A-1 =>(1+tan²A)/(1+1/tan²A){ we know that cot²A = 1/tan²A } =>(1+ tan²A)/ {(tan²A + 1)/tan²A} =>{(tan²A)(1+ tan²A)}/ (tan²A+ 1) => tan²A => sec²A-1 { from the identity sec²A-tan²A = 1}

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Shagun Sehra 9 months, 1 week ago

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Probe that cos^2A+1/1+cot^2A=1

Posted by Muskaan Muskaan 9 months, 1 week ago

CBSE > Class 10 > Mathematics

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In AABC, if LADE = B, then prove that AADE ~ AABC. Also, if AD =7.6 cm, AE = 7.2 cm, BE 4.2 cm and BC = 8.4 cm, find DE

Posted by Muskaan Muskaan 9 months, 1 week ago

CBSE > Class 10 > Mathematics

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if two coconut tree 15 m and 25 meter high are 70 metre apart from then find the height of point of intersection of line joining the top of each tree to foot of opposite tree

Posted by Aditya Raj 9 months, 1 week ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Why π is irrational

Posted by Ashwani Tyagi 9 months, 1 week ago

CBSE > Class 10 > Mathematics

1 answers

Utkarsh Shrivastava 9 months, 1 week ago

Because it has non terminating ana non repeating decimal expansion

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Solve mx-ny=m²+n²,x+y=2m

Posted by Happy Sharma 9 months, 1 week ago

CBSE > Class 10 > Mathematics

1 answers

Shagun Sehra 9 months, 1 week ago

x = m + n y = m - n

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. In a survey, it is found that every fifh person has a vehicle. The probability of a person NOT having a vehicle, is

Posted by Tannu Kumari 9 months, 1 week ago

CBSE > Class 10 > Mathematics

1 answers

Monu Kumar 9 months, 1 week ago

4/5

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In the triangle pqr ab is parallel to QR ifpa equals to 2.4 cm aq equals to 3.6 CM PB = 3.2 CM BR equals to 4.8 cm and ab = 2 cm find QR

Posted by Fjak Nka 9 months, 1 week ago

CBSE > Class 10 > Mathematics

2 answers

Kuldeep Mallick 9 months, 1 week ago

0.4

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Fjak Nka 9 months, 1 week ago

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2xsquare -41x+210

Posted by Manit Mathur 9 months, 1 week ago

CBSE > Class 10 > Mathematics

1 answers

Raunak Singh 9 months, 1 week ago

x= 10 or x= 21/2

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In the given figure, ABCD is a parallelogram. AE divides the line segment BD in the ratio 1 : 2. If BE = 1.5 cm, then find the length of BC

Posted by Vedant Mishra 9 months, 1 week ago

CBSE > Class 10 > Mathematics

0 answers

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The area of a sector of a circle whose radius is r and length of arc is l units is

Posted by Mahika Deshpande 9 months, 1 week ago

CBSE > Class 10 > Mathematics

1 answers

Kaushik Verma 9 months, 1 week ago

1/2×l×r

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Prove that (Tan theta + Sin theta)^2 - (Tan theta - Sin theta)^2.

Posted by Parakram Singh 9 months, 1 week ago

CBSE > Class 10 > Mathematics

2 answers

Manoj Kumar 7 months ago

(Tan theta)^2 - (sin theta)^2

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Yug Purohit 9 months, 1 week ago

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