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Published on: 27/07/2019
Square and Square Roots
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Questions + Answers key
Take MCQ Mathematics Test
1.
How many numbers lie between squares of:
27 and 28
2.
A decimal number is multiplied by itself. If the product is 51.84, then find the number.
3.
In a right triangle ABC, \(\angle\)B = 90°. If AB = 12 cm, BC = 5 cm, then find AC.
4.
For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained.396
5.
Observe the following pattern and supply the missing numbers.
112 = 121
1012 = 10201
101012 =102030201
10101012 =.................................
............. 2 = 10203040504030201
6.
Complete the following crossword puzzle using the given direction.
Direction:
Across:
(1) The product of number by itself two times, is called its _______
(2) If three numbers a, band c are such that a2 + b2= c2 then they are called _____ Triplets.
(3) A number is a when it is a product of the same two numbers.
Down: (4) The numbers 2n, n2-1 and n2 + 1 where n is a natural number show Pythagorean______.
(5) Finding is the inverse operation of squaring a number.
(6) A number which divides a _______ given number exactly is called a or divisor of that number.
7.
Find the least number that must be added to 1500. so as to get a perfect square. Also, find the square root of the perfect square.
8.
The perfect square number out of 2, 3, 4 and 5 is
2
3
4
5
9.
Which of the following is the number of zeros in the square of 900?
3
4
5
2
10.
Which of the following is the difference between the squares of 21 and 22?
21
22
42
43
11.
Which of the following is the number of non-perfect square number between 172and 182?
613
35
34
70
12.
Which of the following is the difference between the squares of two consecutive natural numbers is?
sum of the two numbers
difference of the numbers
twice the sum of the two numbers
twice the difference between the two numbers.
13.
Which of the following is the number of non-perfect square numbers between the squares of the numbers nand n + 1?
n + 1
n
2n
2n+1
14.
A perfect square number having m digits, where m is even will have square root with
\(\frac { m }{ 2 } digits\)
\(\frac { m+1 }{ 2 } digits\)
m + 1 digits
\(\frac { m }{ 3 } digits\)
15.
If \(\sqrt { 4096 } =64\), then the value of \(\sqrt { 4096 } +\sqrt { 40.96 } \) is
70.4
64.4
60.4
68.4
16.
If one member of a Pythagorean triplet is 2m, then other two members are
m, m2 + 1
m2 + 1, m2 - 1
m2, m2 - 1
m2 , m+1
17.
169 is the square of
11
12
13
14
18.
112=_____+_____
19.
1 + 3 + 5 + 7 + 9 + ______ = 62
20.
1 + 3 + 5 + 7 + 9 + ______ = 52
21.
The least number by which 125 be multiplied to make it a perfect square is ____________
22.
The digit at the one's place of 592 is _____________
23.
If n is an odd number of digits of a square-number then the number of digits in its square-root are_______
24.
If n is an even number of digits of a square number then the number of digits in its square root are ________
25.
There are '2n' non-perfect square numbers between the square of the numbers______
26.
0.81
27.
4.41
28.
Can you find the square of the following number 666666672
29.
Using prime factorisation, find the square root of:
81
30.
Find the square of:
35
31.
Can a number ending 1 or 9 be always a square number?
32.
Leela invited some friends for tea on her birthday. Her mother placed some plates and some puris on a table to be served. If Leela places 4 puris in each plate 1 plate would be left empty. But if she places 3 puris in each plate 1puri would be left. Find the number of plates and number of puris on the table.
1.
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.
2.
7.2
3.
We know that, in a right triangle, the side opposite to 90° is hypotenuse.
\(\therefore\) AC is the hypotenuse in \(\Delta\)ABC.
According to Phythagoras theorem,
(Hypotenuse)2= [Sum of the squares of the other two sides]
\(\therefore\) AC2 = AB2 + BC2
\(\Rightarrow\) AC2 = (12)2 + (5)2\(\Rightarrow\) AC2 = 144 + 25
\(\Rightarrow\) AC2 = 169 = (13)2
\(\Rightarrow\)\(\sqrt{{AC}^2}\)=\(\sqrt{{13}^2}\)\(\Rightarrow\) AC = 13 cm
4.
The prime factorisation of 396 is
396 = 2\(\times\)2\(\times\)3\(\times\)3\(\times\)11
By pairing the prime factors, we get
396 = \(\underline { 2\times 2 } \)\(\times\)\(\underline { 3\times 3 } \) \(\times\)11
We see that the prime factor 11 has no pair. So, if we divide 396 by 11, then we get
396 ÷11 = \(\underline { 2\times 2 } \)\(\times\)\(\underline { 3\times 3 } \)
Now each prime factor has a pair. Therefore, 396 + 11 = 36 is a perfect square. Thus, the required smallest number is 11
Also, =\(\sqrt { 36 } \) = 2\(\times\) 3 = 6
5.
According to the first three patterns, we see that given number are in odd digits. When we square the given number we get the number in the odd position. Starting from 1and consecutive increasing number upto the number of odd digits in the given number and then consecutive decreasing number upto 1 and all the even position number 0 exist.
(i) 10101012 = 1020304030201
(ii) 1010101012 = 10203040504030201
6.
1.SQUARE
2.PYTHAGOREAN
3.PERFECT SQUARE
4.TRIPLET
5.SQUARE ROOT
6.FACTOR
7.
We have, 1500
We see that, 382 < 1500 < 392
So, number to be added = 392 - 1500
= 1521 - 1500 = 21
Therefore, the perfect square is 1500 + 21 = 1521 and \(\sqrt { 1521 } \)= 39
So, the required number is 21 and the square root is 39.
8.
4 = 2 x 2 = 22
9.
(b)
4
10.
(d)
43
11.
(c)
34
12.
(a)
sum of the two numbers
13.
(c)
2n
14.
(a)
\(\frac { m }{ 2 } digits\)
15.
(a)
70.4
16.
(b)
m2 + 1, m2 - 1
17.
(c)
13
18.
( )
60 + 61
19.
( )
11+13
20.
( )
11
21.
( )
5
22.
( )
1
23.
( )
\(\frac{n+1}{2}\)
24.
( )
\(\frac{n}{2}\)
25.
( )
n and n +1
26.
( )
0.9
27.
( )
2.1
28.
( )
4444444488888889
29.
( )
9
30.
( )
1225
31.
( )
No
32.
Let the number of plates on the table be y and the number of puris be x.
Then, according to the first condition of the problem
4(y - 1) = x ...(1)
and, according to the second condition of the
problem
3y + 1= x ... (2)
From (1) and (2), we have
4(y - 1) = 3y + 1
⇒ 4y - 4 = 3y + 1
⇒ 4y - 3y = 1 + 4
⇒ y=5
Put y = 5 in (1), we get
x = 4(5) - 4 = 20 - 4 = 16
Hence, the number of plates and number of puris on the table are 5 and 16 respectively.
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