Page 49 - ICSE Math 8

EXERCISE 3.4

1. Find the number of digits in the square roots of the following.
(a) 5,625 (b) 1,537 (c) 15,376 (d) 2,704
2. Find the square roots of the following perfect squares using the long division method.

(a) 441 (b) 6,724 (c) 7,225 (d) 2,809
3. Find the least number that must be subtracted from the following numbers to make them a perfect square.
(a) 2,564 (b) 1,358 (c) 4,227 (d) 3,628
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) 5,120 (d) 6,156
5. Find the greatest number of four digits which is a perfect square.
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6. 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 Root of a Fraction

p p p Square root of the numerator
The square root of a fraction q , q π 0, is q = q = Square root of the denominator .

16 16 4
For example, = = .
25 25 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
Step 1: Convert the mixed fraction into improper fraction, if required.
Step 2: Find the square root of the numerator and the denominator.

Step 3: Arrange them in the form of a fraction.
56
Example 18: Find the square root of 1 169 . 15 13
Solution: 1 56 = 225 1 2 25 1 1 69
169 169 –1 –1
56 225 225
∴ 1 = = 25 125 23 69
169 169 169 –125 –69
We find the square roots of 225 and 169 0 0
separately, as given below.
∴ 225 = 15 and 169 = 13

56 225 225 15 2
⇒ 1 = = = = 1
169 169 169 13 13

243
Example 19: Find the value of .
363
Solution: We have

243 = 243 = 81 = 81 = 9
363 363 121 121 11

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