Square and Square Roots Class 8 MCQ with Answers

Answer: (a) 7

Explanation: If we find the factors of 175 , we would get 175 = 5 x 5 x 7

If we draw out the factors in pairs, we would notice that we have pair of 5 , but 7 is the only single number, which is not in pair.

Therefore if 175 is multiplied by 7 then the product would be a complete square.

Answer: (a) 11449

Explanation: We know that(a + b)²=a²+b²+2ab

When finding the square of a larger number, we can use this equation to break the larger number into parts, whose squares can be easily calculated

We can write 107 as ( 100 + 7 )

So

(107)²=(100+7)²

Applying(a + b)²=a²+b²+2ab

(100)²+7²+ 2 x 100 x 7

= 10000 + 49 + 1400

= 11449

Answer: (a) 4

Explanation: We know that (a−b)²=a²+b²−2ab

If we compare the above equation with the Numerator, we would find that the equation can be re-written as

= (48)²−2×12×48+(12)²

Or we can say that the given equation has value of

a = 48 and b = 12

So we can replace the numeration

48 x 48 – 2 x 12 x 48 + 12 x 12 with (48−12)²=(36)²

Now putting these values in Numerator, we would get

(36)²/(18)² = 1296/324 = 4

Answer: (a) 0.47

Explanation: In order to solve these type of problems, we first need to equate the value which has to be solved 29−−√ of the given equation in the given equation

We can write √18 = 4.24

Replacing 18 by ( 2 x 9 ) in the given equation, and dividing both the sides by 9 , we would get

√(2×9)/(9×9)

= √(18/81)

= √18/9

= 4.24/9

= 0.47

Answer: (b) 48/41

Explanation: Since,

(a²−b²)=(a−b)(a + b)

We can rewrite both the equation as

26² – 22² = {(42)² – (40)²} x Y

( 26 + 22 ) x ( 26 – 22 ) = ( 42 + 40 ) x ( 42 – 40 ) x Y

48 x 4 = 82 x 2 x Y

192 = 164 x Y

Or,

Y = 192/164

Y = 48/41

Answer: (b) 225

Explanation: √x/33 = 5/11

√x = (5×33)/11

√x = 5 x 3

√x = 15

On squaring both the sides

x = 15²

x = 15 x 15

x = 225

Answer: (c) 127

Explanation: (56)²−(55)²+4²

We know that(a²−b²)=(a−b)(a +b)

a = 56 and b = 55

= ( 56 + 55 ) ( 56 – 55 ) + 16

= 111 x 1 + 16

= 111 + 16

= 127

Answer: (b) 112

Explanation: We know that(a)²−(b)²=(a−b)(a +b)

If we compare the above equation to the problem at hand, we find that

a = 16 and b = 12

So we can rewrite the above equation as

16²−12² = ( 16 + 12 ) ( 16 – 12 )

= 28 x 4

= 112

Answer: (b) 15

Explanation: Let the number of rows = Number of students in a row = x

Total number of students = Number of rows x Number of students in a row

Then

x x x = 225

x² = 225

x = √ 225

= √ 3 x 3 x 5 x 5

= 3 x 5

= 15

Hence, the number of rows = Number of students in a row = 15

Answer: (a) 46

Explanation: Funds collected in paisa= 21.16 x 100

= 2116

Funds collected= Numbers of the members of the group x Paisa collected from each member

Or

2116= Numbers of the members of the group x Paisa collected from each member

Let the Number of members of the group= x

Then Paisa collected from each member= x

Substituting these values in the given equation

2116= x x x

x²= 2116

Or,

x = √2116

x = 46

Numbers of the members of the group = 46

Answer: (c) 1000000

Explanation: The numbers which end with 2 , 3, 7 or 8 cannot be the complete squares.

Since the numbers 55557 and 6678 ends with 7 and 8 , therefore, they cannot be perfect square.

If the number of zeros at the end of any number is odd, such a number will not be a perfect square.

As the number of zeros at the end of 3930 are odd, therefore, it will not be a perfect square.

However, 1000000 can be written as = 1000 x 1000

Hence, 1000000 is a perfect square.