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Published on: 03/09/2019
Square and Square Roots
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Questions + Answers key
Take MCQ Mathematics Test
1.
Find the perfect square numbers between 50 and 60
2.
A decimal number is multiplied by itself. If the product is 51.84, then find the number.
3.
If the expression X x 809436 x 809436 be a perfect square, then find the value of x.
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.2925
5.
Without adding, find the sum. 1 + 3 + 5 + 7 + 9
6.
The hypotenuse of a right angled triangle with its base and perpendicular of lengths 3x, 4x respectively is
25x
7 x
5x
16x
7.
A number ending in 9 will have the unit's place of its square as
1
3
9
6
8.
Which of the following is a perfect square?
122
289
258
260
9.
The least number by which 125 be multiplied to make it a perfect square is ____________
10.
\(\sqrt { 2.89 } \) = _____________
11.
There are _____________ perfect square between 1 and 100.
12.
For every natural number m > 1, 2m, m2 - 1, m2 + 1 form a Pythagorean triplet.
13.
The square of 87 will have 3 at the unit's place.
14.
Can you find the square of the following number 666666672
15.
Can you find the square of the following number 66666672
16.
Write the next two square numbers after 441 which end in 1 and their corresponding numbers.
17.
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,
7 X 7 = 49 and 8 X 8 = 64
Hence, there is no perfect square number lying between 50 and 60.
2.
7.2
3.
1
4.
Given number is 2925.
By using prime factorisation, we get
2925 = 3 \(\times\)3 \(\times\)5 \(\times\)5 \(\times\)13
Here, prime factor 13 is unpaired. It is clear that in order to get a perfect square, the given number is divided by 13.
So, the given number should be divided by 13 to make the quotient a perfect square.
Thus, 2925 \(\div \) 13 = 225 is a perfect square .
Now, the prime factor of
225 = 3 \(\times\)3 \(\times\)5 \(\times\)5 = (3 \(\times\)5)2
\(\therefore \) \(\sqrt { 225 } \) = 3 \(\times\)5 = 15
Hence, the square root of 225 is 15.
5.
We have, 1+ 3 + 5 + 7 + 9
Given expression is a sum of consecutive odd numbers.
Here, number of terms in the given expression is n = 5.
We know that, the sum of n consecutive odd numbers is n2
\(\therefore\) The sum of first 5 odd numbers =(5)2 =25
6.
(c)
5x
7.
(a)
1
8.
(b)
289
9.
( )
5
10.
( )
1.7
11.
( )
8
12.
(a)
13.
(b)
14.
( )
4444444488888889
15.
( )
66666672 =44444448888889
16.
( )
The next two square numbers which end in 1 are 841 and 961 and their corresponding numbers are 29 and 31 respectively.
17.
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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