Page 27 - SM inner class 8.cdr

2
2
2
Example 8: 1 =1 Example 9: (i) (11 - (10 ) = 121
)
-
2
3;
2 = + sum of first 2 odd numbers = 121 100
1
3
3 = + 3 + 5 sum of first 3 odd numbers = 21
1
2
+
4 = 1 3 + 5 + 7 sum of first 4 odd numbers = 11 10
+
Prop erty 6: The difference of the square of (ii) (16 ) - (15 ) = 256 225 = 31
2
2
-
two con sec u tive num bers is
+
=16 15
equal to the sum of the num bers. 2 2
-
2
i.e. {(n +1 ) - n 2 } (iii) (36 ) - (35 ) = 1296 1225 = 71
+
= 36 35
= {(n + + )(n + - )} = {(n + ) + }
1
n
1
n
n
1
E xercise 3.1
1. Find which of the follow ing are perfect square:
(i) 121 (ii) 136 (iii) 256 (iv) 441
(v) 76
2. The follow ing numbers are not perfect squares. Give reasons?
(i) 257 (ii) 4592 (iii) 2433 (iv) 5050
(v) 6098
3. Find whether the square of the follow ing numbers are even or odd ?
(i) 431 (ii) 2826 (iii) 8204 (iv) 17779
(v) 99998
4. How many numbers lie between the square of the follow ing numbers
(i) 25; 26 (ii) 56; 57 (iii) 107;108
5. Which of the follow ings are pythag o rean trip let:
(i) 30, 40, 50 (ii) 18, 80, 82 (iii) 15, 60, 65 (iv) 16, 63, 65
Square Root (i) Factorization Method
The square root of a number x is that number The square root of, a perfect square number
which when multiplied by itself gives x as the can be found, by finding the prime factors of
product. the number and grouping them, in pairs.
2
2
)
(i) 3 ´ 3 = 3 = 9 (ii) (– 3) ´ (– 3) = (-3 = 9 Step I: Obtain the given number.
Here 3 and (– 3) are the square roots of 9. Step II: Re solve the given num ber into
The symbol used for square root is prime fac tors by suc ces sive
di vi sion.
9 = ±3 ( read as plus or minus 3)
Step III: Make pairs of prime factors such
Considering only the positive root, we have 9 = 3
that both the factors in each pair
Note: Square of both pos i tive and neg a tive num ber are same. Since the number is a
2
is a pos i tive num ber. Ex am ple: ( )3 = 3 ´ 3 = 9 and perfect square, you will be able to
2
(-3 = -3 ´ -3 = 9
)
make an exact number of pairs of
prime factors.
Finding Square Root
Step IV: Take one factor from each pair.
To find a square root of a number, we have the
Step V: Find the product of factors
following three methods.
obtained in step IV.
(i) Factorization Method (ii) Long Division Method
Step VI: The product obtained in step V is
(iii) Repeated Subtraction Method
the required square root.
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Mathematics In Focus - 8