# KSEEB Solutions for Class 8 Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.7

Students can Download Maths Chapter 5 Squares, Square Roots, Cubes, Cube Roots Ex 5.7 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 5.7

Question 1.
Find the cube root by prime factorisation,
i) 1728
ii) 3375
iii) 10648
iv) 46656
v) 15625
i) 1728 = 2 × 2 × 2 × 6 × 6 × 6 = 12 × 12 × 12
$$\sqrt[3]{1728}=12$$

ii) 3375 = 5 × 5 × 5 × 3 × 3 × 3 = 15 × 15 × 15
$$\sqrt[3]{3375}=15$$

iii) 10648 = 2 × 2 × 2 × 11 × 11 × 11
= 2 × 11 × 2 × 11 × 2 × 11
= 22 × 22 × 22
10648 = 223
∴ $$\sqrt[3]{10648}=22$$

iv) 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
= 4 × 4 × 4 × 9 × 9 × 9
= 4 × 9 × 9 × 4 × 9 × 4
46656 = 36 × 36 × 36 = 363
∴ $$\sqrt[3]{46656}=36$$

v) 15625 = 5 × 5 × 5 × 5 × 5 × 5
= 25 × 25 × 25
15625 = 253
∴ $$\sqrt[3]{15625}=25$$

2. Find the cube root of the following by looking at the last digit and using estimation.

Question (i)
91125
Unit digit of 91125 in 5. Therefore the units digit in its cube root is 5.
Let us split 91125 as 91 and 125. We find that 43 = 64 < 91 < 125 = 53
Hence 403 = 64000 <91125 < 125000 = 503
∴Cube root of 91125 lies between 40 and 50 and units digit is 5 the only such number is 45.
∴ $$\sqrt[3]{91125}=45$$

Question (ii)
166375
Units digit of 166375 is 5. Therefore the units digit of its cube root is 5.
Let us split 166375 as 166 and 375.
53 = 125 < 166 < 216 = 63
Hence 503 = 125000, < 166375 < 216000 = 603
∴ $$\sqrt[3]{166375}$$ lies between 50 and 60. .
Since the units digit is 5 the only such number in 55.
∴ $$\sqrt[3]{166375}=55$$

Question (iii)
704969
The units digit of 704969 is 9. Therefore the units digits of its cube root are 9.
Let us split 704969 as 704 and 969
83 = 512 < 704 < 729 – 93
Hence = 803= 512000 < 704969 < 72900 = 903
∴ $$\sqrt[3]{704969}$$ lies between 80 and 90.
Since the units digits is 9 the only such number is 89.
∴ $$\sqrt[3]{704969}=89$$

3. Find the nearest integer to the cube root of each of the following.
(i) 331776
(ii) 46656
(iii) 373248

Question (i)
331776
603 = 216000 < 331776 < 343000 = 703
Hence $$\sqrt[3]{331776}$$ lies between 60 and 70.
We do not know whether 331776 in a perfect cube or not.
However we may sharpen the bound.
683 = 314432, 693 = 328509
Hence $$\sqrt[3]{331776}$$ lies between 69 and 70
331776 – 328509 = 3267
343000 – 331776 = 11224
331776 in nearer to 693
∴ The closest integer to $$\sqrt[3]{331776}$$ is 69.

Question (ii)
46656
$$\sqrt[3]{46656}$$ lies between 30 and 40 we do not know whether 46656 in a perfect cube or not. However we may sharper the bound
∴ $$\sqrt[3]{46656}=36$$
$$\sqrt[3]{373248}$$ lies between 70 and 80. We do not know whether 373248 is a perfect cube or not.
∴ $$\sqrt[3]{373248}=72$$