NCERT Solution Class 8th Maths Chapter – 5 Squares and Square Roots Exercise – 5.2

NCERT Solution Class 8th Maths Chapter - 5 Squares and Square Roots Exercise - 5.2
Last Doubt

NCERT Solution Class 8th Maths Chapter – 5 Squares and Square Roots

TextbookNCERT
Class8th
SubjectMathematics
Chapter5th
Chapter NameSquares and Square Roots
CategoryClass 8th Maths
Medium English
SourceLast Doubt

NCERT Solution Class 8th Maths Chapter – 5 Squares and Square Roots Exercise – 5.2 In This Chapter we will read about Squares and Square Roots, What is square root kids?, Is a root a zero?, What is a real root?, What are equal roots?, What is a real zero or root?, Can 0 be a real number?, What is polynomial in maths?, What is zeros in algebra?, What is factor form?, What is the formula of real roots?, Is root real or imaginary?, Is 1 a real number?, What is i in math? etc.

NCERT Solution Class 8th Maths Chapter – 5 Squares and Square Roots

Chapter – 5

Squares and Square Roots

Exercise – 5.2

1. Find the square of the following numbers.

(i) 32
(ii) 35
(iii) 86
(iv) 93
(v) 71
(vi) 46

Solution: 

(i) (32)2
= (30 +2)2
= (30)2 + 2×30×2 + (2)2 [Since, (a+b)2 = a2+ 2ab +b2]
= 900 + 4 + 120
= 1024

(ii) (35)2
= (30+5 )2
= (30)2 + 2×30×5 + (5)2 [Since, (a+b)2 = a2+ 2ab +b2]
= 900 + 25 + 300
= 1225

(iii) (86)2
= (80 + 6)2
= (80)2 + 2×80×6 + (6)2[Since, (a+b)2 = a2+ 2ab +b2]
= 1600 + 960 + 36
= 7386

(iv) (93)2
= (90+3)2
= (90)2 + 2×90×3 + (3)2 [Since, (a+b)2 = a2+ 2ab +b2]
= 8100 + 9 + 540
= 8649

(v) (71)2
= (70+1 )2
= (70)2 +2×70×1 [Since, + (1)2 (a+b)2 = a2+ 2ab +b2]
= 4900 + 1 + 140
= 5041

(vi) (46)2
= (40 + 6 )2
= (40)2 + 2×40×6 + (6)2 [Since, (a+b)2 = a2+ 2ab +b2]
= 1600 + 480 + 36
= 2116

2. Write a Pythagorean triplet whose one member is.

(i) 6
(ii) 14
(iii) 16
(iv) 18

Solution:

For any natural number m, we know that 2m, m2–1, m2+1 is a Pythagorean triplet.

(i) 2m = 6
⇒ m = 6/2 = 3
m2–1= 32 – 1 = 9–1 = 8
m2+1= 32+1 = 9+1 = 10
∴ (6, 8, 10) is a Pythagorean triplet.

(ii) 2m = 14
⇒ m = 14/2 = 7
m2–1= 72–1 = 49–1 = 48
m2+1 = 72+1 = 49+1 = 50
∴ (14, 48, 50) is not a Pythagorean triplet.

(iii) 2m = 16
⇒ m = 16/2 = 8
m2–1 = 82–1 = 64–1 = 63
m2+ 1 = 82+1 = 64+1 = 65
∴ (16, 63, 65) is a Pythagorean triplet.

(iv) 2m = 18
⇒ m = 18/2 = 9
m2–1 = 92–1 = 81–1 = 80
m2+1 = 92+1 = 81+1 = 82
∴ (18, 80, 82) is a Pythagorean triplet.

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