Page 37 - SM inner class 8.cdr

Example 6. Find the cube root of (i) 27 ´ 125 3 5 ´ 5 ´ 5 5
(ii) 343 ´ 729. 3 8 ´ 8 ´ 8 = 8

Solution:
Example 8. Find the cube root of 1.331
(i) We have 3 27 125´ = 3 27 ´ 3 125
Solution: We have ( .1 331 )
3
3 3 ´ 3 ´ 3 ´ 3 5 ´ 5 ´ 5 = 3 ´ 5 15
=
1331
(ii) We have 3 343 ´ 729 = 3 343 ´ 3 729 3 ( .331 = 3
1
)
1000
3 7 ´ 7 ´ 7 ´ 3 9 ´ 9 ´ 9 = 7 ´ 9 = 63
´
1331 3 11 ´11 11 11
125 3 = =
Example 7. Find the cube root of . 1000 3 10 ´10 10 10
´
512
125 3 125 3 11
1
)
.
Solution: We have 3 = So, ( .331 = =11
512 3 512 10
E xercise 4.2
1. Find the cube root:
(i) 64 (ii) 343 (iii) 729 (iv) 1728
(v) 9261 (vi) 4096
2. Evaluate the cube root of negative numbers:
(i) -1331 (ii) -512 (iii) -8000 (iv) -3375

(v) -216 (vi) -125
3. Evaluate the cube root of following decimals:
(i) 0.64 (ii) 6.859 (iii) 250.047 (iv) 35.937

(v) 13.824 (vi) 74.088
4. Evaluate the cube root:
(i) 3 8 125´ (ii) 3 216 729´ (iii) 3 64 1000´ (iv) 3 5832 2744´

5. Eval u ate the cube root of follow ing ratio nal numbers:
512 64 2744 125
(i) 3 (ii) 3 (iii) 3 (iv) 3
1728 3375 343 17576
Estimating Cube Root Step IV: Take the smaller number as its
ten’s digit.
This method will work only if the given
number is a perfect cube. The following are the Unit digit of a given Unit digit of cube
steps to estimate the cube root. number root

Step I: Make group of 3 digits from 0 0
unit(one’s) place.This is the 1st 1 1
group.The remaining number 2 8
makes the 2nd group. 3 7
Step II: The unit’s digit of the 1st group 4 4
will decide the unit digit of the 5 5
cube root.( if the unit digit of the 6 6
cube is 6 then the unit digit of cube
7 3
root will also 6 as 6 ´ 6 ´ 6 = 216 ).
8 2
Step III: Find the cube of numbers between
which the 2nd group lie. 9 9
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Mathematics In Focus - 8