Page 70 - Start Up Mathematics_8 (Non CCE)

\ 436.235 @ 20.886 (approx.) \ 12.75 = 3.5707 ª 3.571 (approx.)

upto 3 places of decimal. upto 3 places of decimal.

Example 26: Given 2 = 1.414 and 3 = 1.732, evaluate 225 .
1,014

225 225 15 15 15 6
Solution: = = = = ¥
1,014 169 6 169 ¥ 6 13 6 13 6 6
¥
15 ¥ 6 5 ¥ 2 ¥ 3 5 ¥ 2 ¥ 3
= = =
13 ¥ 6 13 ¥ 2 26
¥
¥
5 1.414 1.732 12.24524
= = = 0.4709 ª 0.471 (approx.)
26 26
EXERCISE 3.8
1. Find the square root of the following upto three places of decimal.
(a) 11 (b) 76 (c) 111 (d) 437.06 (e) 38.004 (f) 7.8
2
(g) 351 (h) 0.00376 (i) 41 (j) 1.05 (k) 0.0000129 (l) 2
9
2. Find the square root of 183.0024 upto five places of decimal.

3. Given 2 = 1.414, 3 = 1.732, 5 = 2.236, evaluate the following:

361 3,136 5,625
(a) (b) (c) (d) 5,000 (e) 19,845
5 15 6
2
4. The area of a square field is 425.31 m . Find the length of the side of the field upto three places of
decimal.

AT a Glance
2
1. If x is any number, then the square of x = x × x = (x) .
2. A number with 2, 3, 7 or 8 at its units place is never a perfect square.
3. A number ending in odd number of zeros is never a perfect square.
4. The square of an even number is always even and an odd number is always odd.
2
5. For any natural number n, sum of the first n-odd natural numbers = n .
2
2
6. There are no natural numbers a and b such that a = 2b .
2
2
7. For every natural number a (a > 1), there exists a Pythagorean triplet (2a, a – 1, a + 1).
2
8. For any given number n, if m is its square root, then n = m or n = m.
x x
9. If x and y are positive numbers, then (a) x ¥ y = x ¥ y (b) = .
y y
Review Exercises

Multiple ChoiCe Questions

1. The square of 9,999 is:
(a) 9,98,001 (b) 99,98,001 (c) 99,80,001 (d) 9,99,80,001

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