Page 160 - Math_Genius_V1.0_C8_Flipbook

E:\Working\Focus_Learning\Math_Genius-8\Open_Files\07_Chapter_6\Chapter_6
\ 06-Jan-2025 Bharat Arora Proof-6 Reader’s Sign _______________________ Date __________

Enrichment

Division Method
Steps Example: Find the cube root of 10648
1. Make groups of three digits of given number 10 648
starting with digit at ones place. Place a bar on
each group.

2. Find the largest cube that is less than or equal Here, the left most group is 10. The largest
3
to the left-most group and write down the cube number whose cube ≤ 10 is 2, since 2 = 8. Write
root of that number as the first digit of the cube 2 as the quotient and subtract 8 from 10.
root of the original number. Let this digit be 2
denoted as a. 4 10 648
–8
2

3. Now, bring down the next group of three digits Here, it is 648, so our new dividend is 2648.
to the right of the remainder. 2

By trial and error, find the next quotient digit 4 10 648
2
denoted as b, such that b(300 × a + 30 × a × b + –8 
b ) ≤ new dividend. 1324 2648
2
2
2
As, 300 × 2 + 30 × 2 × 2 + 2 = 1324
and 2 × 1324 = 2648
4. Now multiply the new divisor by the new ∴ Multiply 1324 by 2 (1324 × 2 = 2648) and subtract
quotient and subtract it from the new dividend. it from the new dividend 2648.
22
4 10 648
–8 M
1324 2648
– 2648

0

So, the cube root of 10648 = 22.
i.e., 3 10648 = 22
Find the cube root of the following using division method.
1. 35937 2. 59319

Example 13: Evaluate: (a) 512 × 2197 (b) 3 96 × 3 144
3
Solution: (a) 3 512 × 2197 = 512 × 3 2197 = 8 × 13 = 104.
3
(b) We observe that 96 and 144 are not perfect cubes. Therefore, 2 96 2 144
we first combine and then factorise them and then use the 2 2 48 2 2 72
36
24
property. 2 12 2 18
3
∴ 3 96 × 3 144 = 96 × 144 = (2 × 2 × 3 ) (2 × 2 × 3 2 ) 2 6 3 9
2
3
×
3
3
3 3 3 3
3
= 3 2 × 2 × 2 × 3 1 1
3
3
3
Thus, 96 × 3 144 = 2 × 2 × 2 × 3 = 24
3
Mathematics-8 158