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Published on: 20/09/2019
Square and Square Roots
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Questions + Answers key
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1.
1 + 3 + 5 + 7 [...]= 16 = 42
1 + 3 + 5 + 7 + 9 [...] = 25 = 52
1 + 3 + 5 + 7 + 9 + 11 [...] = 36 = 62
2.
Check for n = 5, verify
3.
Write the Pythagorean triplet whose one member is 13.
4.
Express 169 as the sum of first 13 odd numbers.
5.
How many numbers lie between squares of:
27 and 28
6.
Express the following as the sum of two consecutive integers. 112
7.
Find the sum of first 4 odd natural numbers and write the number, whose square it is.
8.
Find the square of 0.4
9.
Write the unit's place of 1682
10.
Find the square of 6.1.
11.
How many perfect squares lie between 1 and 50?
12.
Can we say whether the following numbers are perfect squares? How do we know? 7928
Write five numbers which you can decide by looking at their units digit that they are not square numbers.
13.
Can we say whether the following numbers are perfect squares? How do we know? 23453
Write five numbers which you can decide by looking at their units digit that they are not square numbers.
14.
Find the square root of 6280036.
15.
Find the greatest number of three digits that is a perfect square.
1.
1 + 3 + 5 + 7 [Sum of first four odd numbers] = 16 = 42
1 + 3 + 5 + 7 + 9 [Sum of first five odd numbers] = 25 = 52
1 + 3 + 5 + 7 + 9 + 11 [Sum of first six odd numbers] = 36 = 62
2.
n = 5
∴ n + 1 = 6
∴ There are 2n = 2\(\times\)5 = 10 non perfect square numbers between 52 and 62
These are 26, 27, 28, 29, 30, 31, 32, 33, 34 and 35.
3.
When 'n' is a member of a Pythagorean
triplet, then the triplet is
n2 - 1, 2n, n2 + 1
or (132- 1), (2 x 13), (132 + 1)
or (169 - 1), (26), (169 + 1)
or 168, 26 and 170
4.
We have 169 = 132
= Sum of first 13 odd numbers
= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25
= (1 + 25) + (3 + 23) + (5 + 21) + (7 + 19) + (9 + 17) + (11 + 15) + 13
= 26 + 26 + 26 + 26 + 26 + 26 + 13
= (6 x 26) + 13 = 156 + 13 = 169
5.
We know that, between n2 and (n + 1)2, there are 2n non-square numbers.
\(\therefore\) Between 27 and 28, there are 2 x 27, i.e, 54 numbers.
6.
Here , n = 11
∴ \(\frac { { n }^{ 2 }-1 }{ 2 } =\frac { { 11 }^{ 2 }-1 }{ 2 } =\frac { 121-1 }{ 2 } \)
=\(\frac { 120 }{ 2 } \)= 60
and \(\frac { { n }^{ 2 }+1 }{ 2 } =\frac { { 11 }^{ 2 }+1 }{ 2 } =\frac { 121+1 }{ 2 } \)
=\(\frac { 121+1 }{ 2 } \)=61
∴ 112 = 60 + 61 = 121.
7.
Sum of first 4 odd natural numbers is, 1+ 3 + 5 + 7 = 16.
Hence, 16 is a square of 4.
8.
Square of \(0.4\times 0.4=\frac { 4 }{ 10 } \times \frac { 4 }{ 10 } =\frac { 16 }{ 100 } =0.16\)
9.
Since, 8 \(\times\) 8=64. So, the units place of 1682 will be 4.
10.
\(\because \quad 6.1=\frac { 61 }{ 10 } \)
\(\therefore \quad { (6.1) }^{ 2 }={ \left( \frac { 61 }{ 10 } \right) }^{ 2 }=\frac { 61\times 61 }{ 10\times 10 } =\frac { 3721 }{ 100 } =37.21\)
11.
4, 9,16,25,36 and 49 are six perfect squares, which lie between 1 and 50.
12.
We know that, a number ends with 2, 3, 7 or 8 is neverapeIfea square.
The number 7928 ends with 8, which is not one of the end digits of 0, 1, 4, 5, 6 or 9, so it is not a perfect square.
13.
We know that, a number ends with 2, 3, 7 or 8 is neverapeIfea square.
The number 23453 ends with 3, which is not one of the end digits of 0, 1, 4, 5, 6 or 9, so it is not a perfect square.
14.
2506
15.
961
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