Question

EXERCISE 4.2
Use Cordova Smart Class Software on the smart board in class to do Exercise.
1. Find the cube root of the following numbers by prime factorisation method :
(1) 216
(i) 17576
(iii) 39304
(0) 21952
(iv) 54872
(i) 46656
2 Three numbers are in the ratio 2:3:5. The sum of their cubes is 34560. Find the numbers.
3. Find the cube root of 35937 by using (a) Prime factorisation method (b) Without finding prime factors.
4. Find the cube root of the following numbers without finding prime factors:
(1) 157464
(17) 5832
(iii) 19683
(iv) 13824
5. Evaluate :
-2197
4096
1331
(ii) -3.375
(ii) 3-216 x3-15625
9261
6. The volume of a cubical box is 19683 m. Find its edge.
Cordova Learning Series MATHEMATICS-
877​

Answer 1

Answer:

Let, 'n' be the value obtained from 3√216, then as per the definition of cubes, n × n × n = n3 = 216. Since 216 is a perfect cube, we will use here the prime factorisation method, to get the cube root easily.

26 Take the units digit of the smallest number i.e 2. So, The cube root of 17576 is 26.

The cube root of 39304 is 34.

cube root of 21952=2x2x7=28

the cube root of the given number 54872, is 38

36 The square root of 46656 is 216. The cube root of 46656 is 36.

hree numbers in the ratio 2:3:5  

let the common multiplying factor be "x"  

so the three numbers are 2x,3x,5x  

the sum of the cubes are  

8x² + 27x² + 125x² = 34560

160x³ = 34560

x³ = 216  

x = 6  

therefore the three numbers are  

2x = 2*6 = 12

3x = 3*6 = 18

5x = 5*6 = 30

Cube root of 35937 by prime factorization method is 33.

4) a)  the answer is 54.

5832 is said to be a perfect cube because 18 x 18 x 18 is equal to 5832. Since 5832 is a whole number, it is a perfect cube. The nearest previous perfect cube is 4913 and the nearest next perfect cube is 6859 .

Explanation: