Page 66 - Start Up Mathematics_8 (Non CCE)

2
Now, (316) < 1,00,000 < (317) 2
2
\ 1,00,000 = (4,389 – 3,900) less than (317) = 489 less than (317) 2
Thus, the least number to be added is 489.
Hence, the least number of six digits which is a perfect square is 1,00,000 + 489 = 1,00,489.

EXERCISE 3.5

1. Find the number of digits in the square roots of the following:
(a) 5,625 (b) 15,376 (c) 6,11,524 (d) 8,42,724
2. Find the square roots of the following perfect squares using the long division method:
(a) 40,401 (b) 441 (c) 12,34,321 (d) 6,724 (e) 4,80,249
(f) 6,82,276 (g) 64,21,156 (h) 35,70,96,609
3. Find the least number that must be subtracted from the following numbers to make them a perfect
square:
(a) 2,07,978 (b) 4,23,886 (c) 4,85,933 (d) 2,78,840
4. Find the least number that must be added to the following numbers to make them a perfect square:
(a) 5,687 (b) 8,743 (c) 15,120 (d) 6,156
5. Find the greatest number of four digits which is a perfect square.
6. Find the greatest number of three digits which is a perfect square.
7. Find the least number of five digits which is a perfect square.
8. Find the least number of eight digits which is a perfect square.
2
9. The area of a square garden is 8,464 m . A man takes 3 rounds of this garden. Find the distance
covered by him.

Square Roots of Rational Numbers

p r
0
The square root of a rational number q , q π 0 is that rational number , s π which when multiplied by
s
p
itself gives the number q .
r
p r ʈ 2 p
q = s only if Á˜ = q
s
˯
4
ʈ 2 16 16 16 4
For example, Á˜ = 25 fi 25 = 25 = 5
˯
5
The square root of a negative number is not possible because there exists no number whose square is negative.

Steps to find square root 271
Step 1: Simplify the mixed fraction into improper fraction, if required. 2 7 34 41
Step 2: Find the square root of the numerator and the denominator. 4
Step 3: Arrange them in the form of a fraction. 47 334
2,797 329
Example 20: Find the square root of 21 3,364 . 541 541
2,797 73,441
Solution: 21 = 541
3,364 3,364
0

58