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**DAV SOLUTIONS CLASS 8 Secondary Mathematics** Unit 1 Worksheet 1

Question 1 : Which of the following numbers are perfect squares? 11, 16, 32, 36, 50, 64, 75

**Answer: 16,36 and 64 are Perfect Squares .**

**Explanation: As 16 can be written as 4*4 , 36 can be expressed as 36=6*6, 64 can be expressed**

**as 64=8*8 therefore 16,36 and 64 are Perfect Squares .**

Question 2:Which of the following numbers are perfect squares of even numbers? 121, 225, 784, 841, 576, 6561

**Answer: 576 and 784 are perfect square**

**Explanation: Perfect Square of Even Number is always even as Even*Even is also a Even number, therefore 121,225,841 and 6561 are eliminated. Prime factorization of 576 is 2 ^{6} × 3^{2} therefore finding the Square root we get=2^{3}*3^{1} =24 which is an even number. Similarly, The Prime Factorization of 784 is 2^{4} × 7 finding the Square root we get =2^{2} *7=28 which is an even number.**

Question 3: Which of the following numbers are perfect squares? 100, 205000, 3610000, 212300000

**Answer: 100,3610000 are a perfect square. **

**Explanation: Prime factors of 100: 2×2, 5×5 Finding pairs we get=2*5=10 therefore 100 is Square of 10 we can say that 100 is a perfect square. , **

**Prime factors of 20500 : 2×2, 5x5x5, 41 Since there are no pair of 41, 20500 is not a perfect Square, **

** Prime factors of 3610000: 2x2x2x2, 5x5x5x5, 19×19 , here all prime numbers are in pair,3610000=1900*1900 therefore 3610000 is a perfect square, **

** Prime factors of 212300000: 2x2x2x2x2, 5x5x5x5x5, 11, 193 no pair of 193 is available in prime factorization so 21300000 is not a perfect square.**

Question 4:By just observing the digits at one’s place, tell which of the following can be perfect squares? 1026, 1022, 1024, 1027

**Answer: We know that no square number ends in 2, 3, 7 or 8. we can easily infer that 1022 and 1027 can never be a perfect square.**

Question 5: How many non-square numbers lie between the following pairs of numbers?

(i) 7^2 and 8^2 (ii) 10^2 and 11^2 (iv) 80^2 and 81^2 (v) 101^2 and 102^2

(iii) 40^2 and 41^2 (vi) 205^2 and 206^2

**Answer: There are 2n natural numbers lying between two consecutive perfect square numbers n^2 and (n+1)^2i. Here n=7 so there are 27=14 natural number between 7^2 and 8^2ii, Here n= 10 so there are 210=20 natural number 10^2 and 11^2iii, Here n=40 so there are 240=80 natural number 40^2 and 41^2iv, Here n= 80 so there are 280=160 natural number 80^2 and 81^2v, Here n= 101 so there are 2101=202 natural number 101^2 and 102^2vi. Here n= 205 so there are 2205=410 natural number 205^2 and 206^2**

Question 6 :Write down correct number in the box:

i. 100^{2} – 99^{2} =(100-99)(100+99)=199

i. 27^{2} – 26^{2} =(27-26)(27+26)=53

i. 569^{2} – 568^{2} =(100-99)(100+99)=199

**Answer: In general, then, the rule is: y squared minus x squared equals the difference between y and x multiplied by the sum of y and x. Algebraically, we can write this as: y2 – x2 = (y – x) x (y + x)=(y – x) (y + x)——Equation 1Let us assume that y and x are consecutive number,difference between consecutive numbers is 1 so above equation reduces to y+x.i.1002 – 992 =(100-99)(100+99)=199ii. 272 – 262 =(27-26)(27+26)=53iii.5692 – 5682 =(569-568)(569+568)=1137**

Question 7 :Observe the following pattern in the following and find the missing numbers:

Answer: As per the pattern digit in the middle of number is written same times to form a number .In first case 2 is written as 22 ,resultant number is squared and divided by sum of digits.

1234321=4444^{2} / 1+2+3+4+3+2+1

123454321=55555^{2} / 1+2+3+4+5+4+3+2+1

12345654321=666666^{2} / 1+2+3+4+5+6+5+4+3+2+1

Question 8 :Observe the following pattern and fill in the blanks.

1+3 =2^{2}

1+3+5 =3^{2}

1+3+5+7 =4^{2}

1+3+5+7+9=

1+3+5+7+9+11=

1+3+5+7+9+11—–n =

Answer:

Sum of first n consecutive odd digit number is n^{2}

1+3+5+7+9=5^{2} =25

1+3+5+7+9+11=6^{2} =36

1+3+5+7+9+11—–n =n^{2}

Question 9 : Which of the following triplets are Pythagorean? (3, 4, 5), (6, 7, 8), (10, 24, 26), (2, 3, 4)

[Hint: Let the smallest even number be 2m and find in from it. Then, find (2m, m2 — 1, m2 + 1). If you get the triplet, it is Pythagorean.]

Another way of finding a Pythagorean triplet is: If ‘a’, ‘b and ‘c’ are three natural numbers with ‘a’ as the smallest of them, then

(i) If ‘a’ is odd, sum of other two numbers is a^{2} and their difference is 1.

(ii) If ‘a’ is even, sum of other two numbers is a^{2}/2 and their difference is 2.

Answer: (3, 4, 5) Let 2m=4 , m=4/2=2 Now m^{2} -1 =2^{2} -1=3 and m^{2} + 1 =2^{2} +1=5

∴(3, 4, 5) is Pythagorean triplets.

(iii)Taking Triplets (6, 7, 8),Smallest Number=6 2m=6 m=3

Pythagorean triplets are 2m,m^{2} -1,m^{2} + 1 and its value are 6,8,10. Hence (6, 7, 8) is not a pythagorean triplets.

(iv)Taking Triplets (10, 24, 26),Smallest Number=10 2m=10 m=5

Pythagorean triplets are 2m,m^{2} -1,m^{2} + 1 and its value are 10,24,26. Hence (10, 24, 26) is a pythagorean triplets.

(v) Taking Triplets (2, 3, 4),Smallest Number=2 2m=2 m=1

Pythagorean triplets are 2m,m^{2} -1,m^{2} + 1 and its value are 2,0,2. Hence (2, 3, 4) is a not a pythagorean triplets.

- DAV class 8 Maths Book Solutions
- Chapter 1 | Square and Square Roots | Class-8 DAV Secondary Mathematics
- Chapter 2 | Cube and Cube Roots | Class-8 DAV Secondary Mathematics
- Chapter 3 | Exponents And Radicals | Class-8 DAV Secondary Mathematics
- Chapter 4 | Direct And Inverse Variation | Class-8 DAV Secondary Mathematics
- Chapter 5 | Profit, Loss And Discount | Class-8 DAV Secondary Mathematics
- Chapter 6 | Compound Interest | Class-8 DAV Secondary Mathematics
- Chapter 7 | Algebraic Identities | Class-8 DAV Secondary Mathematics
- Chapter 8 | Polynomials | Class-8 DAV Secondary Mathematics
- Chapter 9 | Linear Equations In One Variable | Class-8 DAV Secondary Mathematics
- Chapter 10 | Parallel Lines | Class-8 DAV Secondary Mathematics
- Chapter 11 | Understanding Quadrilaterals | Class-8 DAV Secondary Mathematics
- Chapter 12 | Construction Of Quadrilaterals | Class-8 DAV Secondary Mathematics
- Chapter 13 | Introduction To Graphs | Class-8 DAV Secondary Mathematics
- Chapter 14 | Mensuration | Class-8 DAV Secondary Mathematics
- Chapter 15 | Statistics and Probability | Class-8 DAV Secondary Mathematics
- Chapter 16 | Rotational Symmetry | Class-8 DAV Secondary Mathematics

Aryan— October 21, 2021 at 7:07 PMVery nice

Anonymous— November 25, 2021 at 8:54 AMthere is not worksheet 4 and worksheet 5 and brain treaser so please provide it to us.

Denver singh— November 25, 2021 at 9:00 AMSorry! Will try to update today or by tomorrow.

Anonymous— January 10, 2023 at 11:54 AMBook