KSEEB Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Ex 7.2

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KSEEB Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Ex 7.2

Question 1.
Find the cube root of each of the following numbers by prime factoristor in method.
(i) 64
(ii) 512
(iii) 10648
(iv) 27000
(v) 15625
(vi) 13824
(vii) 110592
(viii) 46656
(ix) 175616
(x) 91125
Solution:
(i) 64 = 2 × 2 × 2 × 2 × 2 × 2
\(\sqrt[3]{64}\) = 2 × 2 = 4

(ii) 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
\(\sqrt[3]{512}\) = 2 × 2 × 2 = 8

(iii) 10648 = 2 × 2 × 2 × 11 × 11 × 11
\(\sqrt[3]{10648}\) = 2 × 11 = 22

(iv) 27000 = 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5
\(\sqrt[3]{27000}\) = 2 × 3 × 5 = 30

(v) 15625 = 5 × 5 × 5 × 5 × 5 × 5
\(\sqrt[3]{15625}\) = 5 × 5 = 25

(vi) 13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
= \(\sqrt[3]{13824}\)
= 2 × 2 × 2 × 3
= 24

(vii) 110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
= \(\sqrt[3]{110592}\)
= 2 × 2 × 2 × 2 × 3
= 48

(viii) 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
= \(\sqrt[3]{46656}\)
= 2 × 2 × 3 × 3
= 36

(ix) 175616 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7
= \(\sqrt[3]{175616}\)
= 2 × 2 × 2 × 7
= 56

(x) 91125 = 3 × 3 × 3 × 3 × 3 × 3 × 5 × 5 × 5
= \(\sqrt[3]{91125}\)
= 3 × 3 × 5
= 45

Question 2.
State true or false.
(i) Cube of any odd number is even.
(ii) A perfect cube does not end with two zeros.
(iii) If the square of a number ends with 5, then its cube ends with 25.
(iv) There is no perfect cube which ends with 8.
(v) The cube of a two-digit number may be a three-digit number.
(vi) The cube of a two-digit number may have seven or more digits.
(vii) The cube of a single-digit number may be a single-digit number.
Solution:
(i) False
(ii) True
(iii) True
(iv) False
(v) False
(vi) False
(vii) True

Question 3.
You are told that 1,331 is a perfect cube. Can you guess without factorisation what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768.
Solution:
For 1331: Unit’s digit of the cube root of 1331 is 1. As unit’s digit of the cube root of the number ending in 1 is 1. After striking three digits from the right of 1331, we get the number 1. Since, 1³ = 1, so ten’s digit of the cube root of a given number is 1
∴ √1331 = 11

For 4913: Unit’s digit of the cube root of 4913 is 7, As unit’s digit of the cube root of the number ending in 3 is 7. After striking three digits from the right of 4913, we get 4. As 1³ = 1 and 2³ = 8. So, 1³ < 4 < 2³
∴ Ten’s digit of the cube root of 4913 is 1
∴ \(\sqrt[3]{4913}\) = 17

For 12167: Unit’s digit of the cube root of 12167 is 3. As unit’s digit of the cube root of numbers ending in 7 is 3. After striking three digits from the right of 12167, we get the number 12.
As 2³ = 8
and 3³ = 27, so, 2³ < 12 < 3³
Hence, ten’s digit of cube root of 12167 is = \(\sqrt[3]{32768}\) = 23

For 32768: Unit’s digit of the cube root of 32768 is 2. As unit’s digit of the cube root of the numbers ending in 8 is 2. After striking three digits from the right of 32768, we get the number 32.
As 3³ = 27
and 4³ = 64, so, 3³ < 32 < 4³
So, the ten’s digit of the cube root of 32768 is 3
∴ \(\sqrt[3]{32768}\) = 32.