## RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.3

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.3

**Other Exercises**

- RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.1
- RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.2
- RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.3
- RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.4
- RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5
- RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6
- RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7
- RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8
- RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9

**Question 1.**

**Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication :**

**(i) 25**

**(ii) 37**

**(iii) 54**

**(iv) 71**

**(v) 96**

**Solution:**

(i) (25)^{2}

**Question 2.**

**Find the squares of the following numbers using diagonal method :**

**(i) 98**

**(ii) 273**

**(iii) 348**

**(iv) 295**

**(v) 171**

**Solution:**

**Question 3.**

**Find the squares of the following numbers :**

**(i) 127**

**(ii) 503**

**(iii) 451**

**(iv) 862**

**(v) 265**

**Solution:
**(i) (127)

^{2}= (120 + 7)

^{2 }{(a + b)

^{2}= a

^{2}+ lab + b

^{2}}

= (120)

^{2}+ 2 x 120 x 7 + (7)

^{2 }= 14400+ 1680 + 49 = 16129

(ii) (503)^{2} = (500 + 3)^{2
}{(a + b)^{2} = a^{2} + lab + b^{1}}

= (500)^{2} + 2 x 500 x 3 + (3)^{2
}= 250000 + 3000 + 9 = 353009

(iii) (451)^{2} = (400 + 51)^{2
}{(a + b)^{2} = a^{2} + lab + b^{2}}

= (400)^{2} + 2 x 400 x 51 + (5l)^{2
}= 160000 + 40800 + 2601 = 203401

(iv) (451)^{2} = (800 + 62)^{2
}{(a + b)^{2} = a^{2} + lab + b^{2}}

= (800)^{2} + 2 x 800 x 62 + (62)^{2
}= 640000 + 99200 + 3844 = 743044

(v) (265)^{2}

{(a + b)^{2} = a^{2} + 2ab + b^{2}}

(200 + 65)^{2} = (200)^{2} + 2 x 200 x 65 + (65)^{2
}= 40000 + 26000 + 4225 = 70225

**Question 4.
**

**Find the squares of the following numbers**

**(i) 425**

**(ii) 575**

**(iii) 405**

**(iv) 205**

**(v) 95**

**(vi) 745**

**(vii) 512**

**(viii) 995**

**Solution:**

(i) (425)

^{2 }Here n = 42

∴ n (n + 1) = 42 (42 + 1) = 42 x 43 = 1806

∴ (425)

^{2}= 180625

(ii) (575)^{2
}Here n = 57

∴ n (n + 1) = 57 (57 + 1) = 57 x 58 = 3306

∴ (575)^{2} = 330625

(iii) (405)^{2
}Here n = 40

∴ n (n + 1) = 40 (40 + 1) -40 x 41 = 1640

∴ (405)^{2} = 164025

(iv) (205)^{2
}Here n = 20

∴ n (n + 1) = 20 (20 + 1) = 20 x 21 = 420

∴ (205)^{2} = 42025

(v) (95)^{2
}Here n = 9

∴ n (n + 1) = 9 (9 + 1) = 9 x 10 = 90

∴ (95)^{2} = 9025

(vi) (745)^{2}

Here n = 74

∴ n (n + 1) = 74 (74 + 1) = 74 x 75 = 5550

∴ (745)^{2} = 555025

(vii) (512)^{2
}Here a = 1, b = 2

∴ (5ab)^{2} = (250 + ab) x 1000 + (ab)^{2
}∴ (512)^{2} = (250 + 12) x 1000 + (12)^{2
}= 262 x 1000 + 144

= 262000 + 144 = 262144

(viii) (995)^{2
}Here n = 99

∴ n (n + 1) = 99 (99 + 1) = 99 x 100 = 9900

∴ (995)^{2} = 990025

**Question 5.
**

**Find the squares of the following numbers using the identity (a + b)1 = a2 + lab + b1**

**(i) 405**

**(ii) 510**

**(iii) 1001**

**(iv) 209**

**(v) 605**

**Solution:**

a + b)

^{2}= a

^{2}+ lab + b

^{2 }

(i) (405)^{2} = (400 + 5)^{2
}= (400)^{2} + 2 x 400 x 5 + (5)^{2
}= 160000 + 4000 + 25 = 164025

(ii) (510)^{2} = (500 + 10)^{2
}= (500)^{2} + 2 x 500 x 10 x (10)^{2
}= 250000 + 10000 + 100

= 260100

(iii) (1001)^{2} = (1000+1)^{2
}= (1000)^{2} + 2 X 1000 x 1 + (1)_{
}= 1000000 + 2000 + 1

=1002001

(iv) (209)^{2} = (200 + 9)^{2
}= (200)^{2} + 2 x 200 x 9 x (9)^{2}

= 40000 + 3600 +81

= 43681

(v) (605)^{2} = (600 + 5)^{2
}= (600)^{2} + 2 x 600 x 5 +(5)^{2}_{
}= 360000 + 6000 25

=366025

**Question 6.
**

**Find the squares of the following numbers using the identity (a – b)**

^{2}= a^{2}– 2ab + b^{2}:**(i) 395**

**(ii) 995**

**(iii) 495**

**(iv) 498**

**(v) 99**

**(vi) 999**

**(vii) 599**

**Solution:**

a – b)

^{2}= a

^{2}– lab + b

^{2}

(i) (395)^{2} = (400 – 5)^{2
}= (400)^{2} – 2 x 400 x 5 + (5)^{2
}= 160000-4000 + 25

= 160025-4000

= 156025

(ii) (995)^{2} = (1000 – 5)^{2}

= (1000)^{2} – 2 x 1000 x 5 + (5)^{2
}= 1000000- 10000 + 25

= 1000025- 10000

= 990025

(iii) (495)^{2} = (500 – 5)^{2
}= (500)^{2} – 2 x 500 x 5 + (5)^{2
}= 250000 – 5000 + 25

= 250025 – 5000

= 245025

(iv) (498)^{2} = (500 – 2)^{2
}= (500)^{2} – 2 x 500 x 2 + (2)^{2
}= 250000 – 2000 + 4

= 250004 – 2000

= 248004

(v) (99)^{2} = (100 – l)^{2
}= (100)^{2} – 2 x 100 x 1 + (1)^{2}

= 10000 – 200 + 1

= 10001 – 200

= 9801

(vi) (999)^{2} = (1000- l)^{2
}= (1000)^{2} – 2 x 1000 x 1+ (1)2

= 1000000-2000+1

= 10000001-2000=998001

(vii) (599)^{2} = (600 – 1)^{2
}= (600)^{2 }-2 x 600 X 1+ (1)2

= 360000 -1200+1

= 360001 – 1200 = 358801

**Question 7.
**

**Find the squares of the following numbers by visual method :**

**(i) 52**

**(ii) 95**

**(iii) 505**

**(iv) 702**

**(v) 99**

**Solution:**

(a + b)

^{2}= a

^{2}– ab + ab + b

^{2 }(i) (52)

^{2}= (50 + 2)

^{2 }= 2500 + 100 + 100 + 4

= 2704

(ii) (95)

^{2}= (90 + 5)

^{2 }= 8100 + 450 + 450 + 25

= 9025

(iii) (505)

^{2}= (500 + 5)

^{2 }= 250000 + 2500 + 2500 + 25

= 255025

(iv) (702)

^{2}= (700 + 2)

^{2 }= 490000 + 1400+ 1400 + 4

= 492804

(v) (99)

^{2}= (90 + 9)

^{2 }= 8100 + 810 + 810 + 81

= 9801

Hope given RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.3 are helpful to complete your math homework.

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