Which of the following natural numbers are perfect squares? Give reasons in support of your answer.
(i) 729
(ii) 5488
(iii) 1024
(iv) 243
Show that each of the following numbers is a perfect square. Also, find the number whose square is the
given number.
(i) 1296
(ii) 1764
(iii) 3025
(iv) 3969
Find the smallest natural number by which 1008 should be multiplied to make it a perfect square.
Solution:
Find the smallest natural number by which 5808 should be divided to make it a perfect square. Also, find
the number whose square is the resulting number.
Write five numbers which you can decide by looking at their one’s digit that they are not square
numbers.
What will be the unit digit of the squares of the following numbers?
(i) 951
(ii) 502
(iii) 329
(iv) 643
(v) 5124
(vi) 7625
(vii) 68327
(viii) 95628
(ix) 99880
(x) 12796
The following numbers are obviously not perfect. Give reason.
(i) 567
(ii) 2453
(iii) 5298
(iv) 46292
(v) 74000
The square of which of the following numbers would be an odd number or an even number? Why?
(i) 573
(ii) 4096
(iii) 8267
(iv) 37916
How many natural numbers lie between the square of the following numbers?
(i) 12 and 13
(ii) 90 and 91
Without adding, find the sum.
(i) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29
(i) Express 64 as the sum of 8 odd numbers.
(ii) 121 as the sum of 11 odd numbers.
Express the following as the sum of two consecutive integers.
(i) 19^{2} (ii) 33^{2} (iii) 47^{2}
Find the squares of the following numbers without actual multiplication:
(i) 31
(ii) 42
(iii) 86
(iv) 94
Find the squares of the following numbers containing 5 in unit’s place:
(i) 45
(ii) 305
(iii) 525
Write a Pythagorean triplet whose one number is
(i) 8
(ii) 15
(iii) 63
(iv) 80
Observe the following pattern and find the missing digits:
\begin{array}{l} 21^{2}=441 \\ 201^{2}=40401 \\ 2001^{2}=4004001 \\ 20001^{2}=4-4-1 \\ 200001^{2}= \end{array}
Observe the following pattern and find the missing digits
9^{2}=81
\begin{array}{l} 99^{2}=9801 \\ 999^{2}=998001 \\ 9999^{2}=99980001 \\ 99999^{2}=9-8-01 \\ 999999^{2}=9–0-1 \end{array}
\begin{array}{l} 7^{2}=49 \\ 67^{2}=4489 \\ 667^{2}=444889 \\ 6667^{2}=44448889 \\ 66667^{2}=4-8-9 \\ 666667^{2}=4 \ldots-8-8 \end{array}
By repeated subtraction of odd numbers starting from 1, find whether the following numbers are perfect
squares or not? If the number is a perfect square then find its square root:
Find the square roots of the following numbers by prime factorization method:
(i) 784
(ii) 441
(iii) 1849
(iv) 4356
(v) 6241
(vi) 8836
(vii) 8281
(viii) 9025
(i) 9 67/121
(ii) 17 13/36
(iii) 1.96
(iv) 0.0064
For each of the following numbers, find the smallest natural number by which it should be multiplied so
as to get a perfect square. Also, find the square root of the square number so obtained:
(i) 588
(ii) 720
(iii) 2178
(iv) 3042
(v) 6300
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