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Squares and Square Roots

    Exercise 5.1

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8th class > Squares and Square Roots > Exercise 5.1

Exercise 5.1

  1. What will be the unit digit of the squares of the following numbers?

Instructions
  1. The following numbers are obviously not perfect squares. Give reason.

Instructions

Condition: Natural numbers ending in the digits , , , and are not perfect squares. (Enter numbers in increasing order)
(i) 1057 a perfect square as it with the digit .
(ii) 23453 a perfect square as it with the digit .
(iii) 7928 a perfect square as it with the digit .
(iv) 222222 a perfect square as it with the digit .
(v) 64000 a perfect square as it with the digit and the number of zeroes at the end are .
(vi) 89722 a perfect square as it with the digit .
(vii) 222000 a perfect square as it with the digit and the number of zeroes at the end are .
(viii) 505050 a perfect square as it with the digit and the number of zeroes at the end are .
  1. The squares of which of the following would be odd numbers?

Instructions

431
2826
7779
82004
Odd
Not Odd
  1. Observe the following pattern and find the missing digits.

Instructions

112=121

  • 112 gives us 121.
  • 1012 gives us 10201.
  • Further on, 10012 gives us 1002001. You might have notice a pattern.
  • Now, we get: 1000012 = .
  • And 100000012 = .
  • We have completed the pattern.
  1. Observe the following pattern and supply the missing numbers.

Instructions

112=121

  • 112 gives us 121.
  • 1012 gives us 10201.
  • Further on, 101012 gives us 102030201. You might have notice a pattern.
  • Now, we get: 10101012 = .
  • And = 1020304050403020.
  • We have completed the pattern.
  1. Using the given pattern, find the missing numbers.

Instructions

12+22+22=32

  • Notice the above pattern.
  • Further on, we have.
  • The even further sequence is as shown. You might have notice a pattern.
  • Now, we get: 42+52+ = 212
  • 52 + + 302 = 312
  • 62+72 + =
  • We have completed the pattern.
  1. Without adding, find the sum:

Instructions

(i) 1 + 3 + 5 + 7 + 9
Since, we have the sum of the first five odd numbers, the result is i.e. .
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
Since, we have the sum of the first odd numbers, the result is i.e. .
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
Since, we have the sum of the first odd numbers, the result is i.e. .
  1. (i) Express 49 as the sum of 7 odd numbers.

(ii) Express 121 as the sum of 11 odd numbers.

Instructions

Express 49 as the sum of 7 odd numbers.
Sum of first n odd natural numbers is . We also have 49 =
Upon, solving we get , 49 = + + + + + + i.e. the sum of the first odd numbers.
Express 121 as the sum of 11 odd numbers.
We know that 121 =
Upon, solving we get , 49 = + + + + + + + + + + i.e. the sum of the first odd numbers.
  1. How many numbers lie between squares of the following numbers?

Instructions

(i) 12 and 13
We know 122 = and 132 = . So, a total of numbers lie in between.
(ii) 25 and 26
We know 252 = and 262 = . So, a total of numbers lie in between.
(iii) 99 and 100
We know 992 = and 1002 = . So, a total of numbers lie in between.