Page 53 - ICSE Math 8

AT A GLANCE
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¾ If x is any number, then the square of x = x × x = (x) .
¾ A number with 2, 3, 7 or 8 at its units place is never a perfect square.
¾ A number ending in odd number of zeros is never a perfect square.
¾ The square of an even number is always even and that of an odd number is always odd.
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¾ For any natural number n, sum of the first n-odd natural numbers = n .
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¾ For any given number n, if m is its square root, then n = m or n = m.
x x
¾ If x and y are positive numbers, then (a) x × y = x × y (b) = .
y y

¾ The square root of negative number is not possible as there exists no number whose square root is negative.
¾ To find square root of decimal numbers, the numbers in the decimal part are paired from left to right,
and from right to left in the integral part.

MENTAL MATHS

1. Choose the correct option.
(a) The square of 9,999 is:
(i) 9,98,001 (ii) 99,98,001 (iii) 99,80,001 (iv) 9,99,80,001

(b) The smallest number by which 98 must be divided to make it a perfect square is:
(i) 2 (ii) 3 (iii) 7 (iv) 6

(c) 0.09 is equal to:
(i) 0.03 (ii) 0.3 (iii) 0.003 (iv) 0.034
(d) The smallest number that must be subtracted from 176 to make it a perfect square is:
(i) 16 (ii) 7 (iii) 10 (iv) 4

(e) 7,225 is equal to:
(i) 75 (ii) 85 (iii) 65 (iv) 95
2. Write True or False.
(a) The square of an odd number is always odd.
(b) The sum or difference of two square numbers is a square number.
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(c) The value of × 5.76 is 7.
0.09
(d) For positive numbers x and y, x × y = xy .
3. Fill in the blanks.

(a) A number ending in 2, 3, 7 or 8 is ______________ a perfect square.
(b) On dividing a perfect square by 4, the remainder is ___________ or ______________.
(c) A number ending in ______________ number of zeros is never a perfect square.

(d) The sum 1 + 3 + 5 + 7 + 9 + 11 + 13 = ______________.
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(e) The value of 100 – 99 is __________________.
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