Page 28 - SM inner class 8.cdr

Example 10: Find the square root of 64. right of the remainder. So the new
Solution: Prime factorization of 64 dividend is 329.
2
2 64
2 7 29
2 32 2 –4
2 16 4 3 2 9

2 8 Step 4: Add the divisor 2 and quotient 2
2 4 that gives us 4.
2 2 Step 5: Think of a largest number and fill
it in the blank in such a way that
1
the product of a new divisor and
= 2 ´ 2 ´ 2 ´ 2 ´ 2 ´ 2 this digit is equal to or less than
= 2 2 ´ 2 2 ´ 2 2 329(new dividend).
= 2 ´ 2 ´ 2 = 8 27
2 7 29
2. Long Division Method 2 –4

When the numbers are very large, even the 47 3 2 9
prime factorization method is tedious and time 7 –3 2 9
consuming so we use the long division method 0
which is explained in the following steps. In this case 4 7 ´ 7 = 329.
Steps of Long Division Method for As 47 ´ 7 = 329 so we choose the
new digit as 7. Get the remainder.
Finding Square Roots:
Step 6: Since the remainder is 0 and no
Example 11. Find square root of 729 by long
digits are left in the given number,
division method.
\ 729 = 27.
Solution:
Example 12. Find the square root of 1024.
Step 1: Place a bar over every pair of digits
starting from the unit digit. If the Solution: 32
number of digits in it is odd, then 3 10 2 4
the left-most single digit too will –9
have a bar. As we have, 729.So 1st 62 1 2 4
bar is on 29 and 2nd bar is on 7. –1 2 4
0
7 29
\ 1024 = 32
Step 2: Find the largest number whose
square is less than or equal to the Example 13. Find the square root of 15129.
1st number,here it is ‘7’. Solution:
2
(2 < 7 < 3 2 ). So here we take 2. 123
Divide and get the remainder (3 in 1 1 51 29
this case). +1 –1
2 22 51
2 7 29 +2 – 44
+2 –4
243 729
4 3 3 729
Step 3: Bring down the number under the 0
next bar (i.e., 29 in this case) to the
\ 15129 =123

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Mathematics In Focus - 8