KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4

Students can Download Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka Board Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4

1. Find the square root of the following numbers by factorization.

Question (i)
196
Answer:
196 = 2 × 2 × 7 × 7
= 2 × 7 × 2 × 7
196 = 14 × 14
√196 = 14
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 1

Question (ii)
256
Answer:
256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
256 = 16 × 16
√256 = 16
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 2

Question (iii)
10404
Answer:
10404 = 2 × 2 × 3 × 3 × 17 × 17
= 2 × 3 × 17 × 2 × 17
10404 = 102 × 102
√10404 = 102
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 3

Question (iv)
1156
Answer:
1156 = 2 × 2 × 17 × 17
= 2 × 17 × 2 × 17
1156 = 34 × 34
√1156 = 34
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 4

Question (v)
13225
Answer:
13225 = 5 × 5 × 23 × 23
= 5 × 23 × 5 × 23
13225 = 115 × 115 7
√13225 = 115
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 5

2. Simplify

Question (i)
√100 + √36
Answer:
√100 + √36 = 10 + 6 = 16

Question (ii)
√1360 + 9
Answer:
√1360 + 9 = √1369
√1369 = 37 × 37
√1369 = 37
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 6

Question (iii)
√2704+√144+√289
Answer:
2704 = 2 × 2 × 2 × 2 × 13 × 13
= 2 × 2 × 13 × 2 × 2 × 13
2704 = 52 × 52
√2704 =52
√144 = 12 and √289 = 17
∴ √2704 + √144 + √289 = 52 + 12 + 17 = 81

Question (iv)
√225 – √25
Answer:
15 – 5=10

Question (v)
√1764 – √1444
Answer:
1764
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 7
1764 = 2 × 2 × 3 × 3 × 7 × 7
=2 × 3 × 7 × 2 × 3 × 7
1764 = 42 × 42
√l764 = 42
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 8
1444 = 2 × 2 × 19 × 19
= 2 × 19 × 2 × 19
1444 = 38 × 38
√1444 = 38
∴√l764 – √1444 = 42 – 38 = 4

Question (vi)
√169 × √361
Answer:
√169 × √361 = 13 × 19 = 247

Question 3.
A square yard has an area 1764 m2. From a corner of this yard, another square part of area 784 m2 is taken out for public utility. The remaining portion is divided into equal square parts. What is the perimeter of each of these equal parts?
Answer:
The area of the remaining portion= 1764 – 784 = 980 m2
It is divided into 5, equal square parts
∴ Each square part = \(\frac{980}{5}\) = 196 m2
Area of each square part = 196 m2
(side)2 = 196
side = √196
side = 14.
The length of each side of the square = 14m
Perimeter = 4 side = 4 × 14 = 56m

4. Find the smallest positive integer with which one has to multiply each of the following numbers to get a perfect square.

Question (i)
847
Answer:
847 = 7 × 11 × 11
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 9
Here we observe that 7 appears only once.
∴The required number of multiplied is 7.

Question (ii)
450
Answer:
450 = 2 × 5 × 5 × 3 × 3
Here we observe that 2 appears only once
∴ The required number is 2.
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 10

Question (iii)
1445
Answer: 1445 = 5 × 17 × 17
Here we observe that 5 appears only once
∴ The required number of multiplied is 5.
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 11

Question (iv)
1352
Answer:
1352 = 2 × 2 × 2 × 13 × 13
= 2 × 13 × 2 × 13 × 2
= 26 × 26 × 2
Here we observe that 2 appears only once in the product.
∴ The required number multiplier is 2
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 12

5. Find the largest perfect square factor of each of the following numbers.

Question (i)
48
Answer:
48 = 2 × 2 × 2 × 2 × 3
48= 16 × 3
∴ Largest perfect square factor is 16.
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 13

Question (ii)
11280
Answer:
11280 = 2 × 2 × 2 × 2 × 3 × 5 × 47
= 16 × 3 × 5 × 47
∴ Largest perfect square factor is 16.
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 14

Question (iii)
729
Answer:
729 = 3 × 3 × 3 × 3 × 3 × 3
= 27 × 27
= 729
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 15
∴ Largest perfect square factor is 729.

Question (iv)
1352
Answer: 1352 = 2 × 2 × 2 × 13 × 13
= 2 × 13 × 2 × 3 × 2
= 26 × 26 × 2
= 676 × 2
KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.4 16
∴ The largest perfect square factor is 676

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