MCQ Questions for Class 8 Maths Squares And Square Roots Quiz 6

A gardener has

$1000$ plants.He wants to plants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.

0%
12
0%
24
0%
11
0%
23

Explanation

If the number of rows and number of columns are to be equal, then the total number of trees will be in the form of x², which is nothing but a perfect square.

As 1000 is not a perfect square, you need to check for a perfect square above and nearest to 1000.

It's 1024, which is square of 32. $\text{ So he needs to add 24 more trees to get 1024.}$

Find the square root of 12.25.

0%
3.5
0%
4.25
0%
4.5
0%
3

Area of a square plot is

$2304$

$\displaystyle m^{2}$ . Find the side of the square plot.

0%
$48$ m
0%
$33.9$ m
0%
$39.9$ m
0%
$42$ m

Explanation

Area of square plot

$= 2304$

$\displaystyle m^{2}$
Therefore side of the square plot

$\displaystyle \sqrt{2304}$ m
We find that

$\displaystyle \sqrt{2304}=48=\sqrt {2\times2\times2\times2\times2\times2\times2\times2\times3\times3}$
Thus the side of the square plot is

$48 m$ .

Perfect square numbers between

$20$ and

$30$ is/are

0%
$21, 25, 28$
0%
$27, 29, 25$
0%
only $25$
0%
only $29$

Explanation

The perfect square between

$20$ and

$30$ is only

$25$ .
That is,

$4 \times 4 = 16$

$5 \times 5 = 25$

$6 \times 6 = 36$

$25$ is the only perfect square which falls between $20$ and $30$ .

Therefore, option C is correct.

Which of the following are perfect squares?

0%
$25, 36, 49$
0%
$64, 19, 72$
0%
$18, 30 , 42$
0%
$45, 32, 42$

Find the numbers whose square will end with digit

$1$ .

0%
$(49)^2, (19)^2$
0%
$(18)^2, (48)^2$
0%
$(15)^2, (25)^2$
0%
$(24)^2, (42)^2$

Explanation

The numbers which will have $1$ at their unit place in their squares are the numbers ends with $1$ or $9$

Because $1\times1$ $=$ $1$ and $9 \times 9 = 81$

Hence, Option A is correct answer.

The numbers having

$1$ or

$9$ in the units place, then its square ends with_______.

0%
$9$
0%
$0$
0%
$1$
0%
$6$

Explanation

$9 \times 9 = 8\underline{1}$

$11 \times 11 = 12\underline{1}$ ......(last digit is

$1$ )
Therefore, option C is the correct answer.

Find the square root of

$225$ .

0%
12
0%
13
0%
15
0%
None of these

Explanation

Here, $225 = 3 \times 3 \times 5 \times 5 = (3 \times 5)^2 = (15)^2$

Therefore, option C is the correct answer.

Numbers other than the perfect square numbers are not:

0%
square numbers
0%
non square numbers
0%
both A and B
0%
none of the above

If the square ends with 6, then the number has ___ or ___ in the units place.

0%
$2$ or $8$
0%
$4$ or $6$
0%
$1$ or $9$
0%
$3$ or $7$

Explanation

For example,

$24 \times 24 = 57\underline{6}$

$36 \times 36 = 129\underline{6}$ ( square ends with 6)
Therefore, B is the correct answer.

$(64)^2$ would have digit ____ at units place.

0%
7
0%
6
0%
9
0%
1

Explanation

In $(64)^2$ , the digit in unit's place is the last digit at the multiplication of

$4 \times 4 = 1\underline{6}$

So, $6$ at units place

Therefore, B is the correct answer.

The units place of a number is

$2$ or

$8$ , then the last digit of its square is always _____.

0%
$4$
0%
$6$
0%
$0$
0%
$2$

Explanation

$22 \times 22 = 484 , 18 \times 18 = 324, 2\times 2 = 4 , 8 \times 8 = 64$
Last digit in the squares of numbers in both the cases is 4.
Therefore, A is the correct answer.

For an odd number

$427$ , the square of this odd number will be ____.

0%
even
0%
odd
0%
negative
0%
none of these

Explanation

Since, the last digit of number $427$ is $7$ , $7$ being an odd number the whole square number will be odd because $7 \times 7 = 49$

Thus, square root of an odd number is odd

Therefore, option B is the correct answer.

If the square ends with 1, then the number has ___ or ___ in the units place.

0%
$3$ or $7$
0%
$4$ or $6$
0%
$2$ or $8$
0%
$1$ or $9$

Explanation

For example,

$11 \times 11 = 12\underline{1}$

$19 \times 19 = 36\underline{1}$ ( square ends with 1)
Therefore, D is the correct answer.

When a square number ___ in

$6$ , the number whose square it is, will either have

$4$ or

$6$ in ___ place.

0%
ends, units
0%
starts, units
0%
ends, tens
0%
starts, tens

Explanation

Only those numbers, when squared will have 6 at their unit place which end with

$4$ or

$6$

Because

$4\times4$

$=$

$16$

and

$6\times6$

$=$

$36$

Hence, Option A is correct answer.

If the square ends with 9, then the number has ___ or ___ in the units place.

0%
$3$ or $7$
0%
$4$ or $5$
0%
$9$ or $1$
0%
None of these

Explanation

Only those numbers, when squared will have 9 at their unit place are

$3$ and

$7$ .

Because

$3\times3$

$=$

$9$

and

$7\times7$

$=$

$9$

Hence, Option A is correct answer.

Find perfect square numbers between

$140$ &

$150$ .

0%
$144$
0%
$142$
0%
$86, 89$
0%
None of the above

Explanation

We know

$11^2 = 121$ comes before $140$

$12^2 = 144$ lies between $140$ $\&$ $150$

$13^2 = 169$ lies after $150$

Only $144$ lies between $140$ & $150$

So $144$ is the only perfect square number between $140$ & $150$

A school was having a gathering. The organizing teacher wanted the students to be seated in the same number of rows and columns. The number of students were

$10000$ . Find the number of rows and columns.

0%
$80$
0%
$90$
0%
$100$
0%
$10$

Explanation

To get the number of row and column, we need to find square root of

$10000$

Number of row

$=$ Number of column

$\sqrt{10000}$

$=$

$100$

Hence, Option C is correct.

Which smallest whole number is to be multiplied to

$2028$ to get a perfect square number?

0%
$4$
0%
$3$
0%
$2$
0%
$6$

Explanation

To find out what needs to be multiplied to

$2028$ to make it a perfect square, we need to find out the factors of

$2028$ .

Hence factors of 2028 are :

$2028 = \underline{2 \times 2} \times \underline{13\times 13} \times 3$
Prime factor

$3$ is not in pairs, so

$3$ has to be multiplied to get the perfect square i.e.

$2028 \times 3 = 6084$

Hence the answer is C.

Find perfect square numbers between

$80$ &

$90$ .

0%
$80, 84$
0%
Only $81$
0%
86, 89
0%
None of the above

Explanation

Only $81$ is a perfect square number between $80$ & $90$ .

$9^2= 81$ ,

$10^2 = 100$ , before its $8^2= 64$ .

$(64, 81, 100$ ) only $81$ lies between $80$ & $90$ .

Therefore, B is the correct answer.

The square root of

$1764$ is ____.

0%
$42$
0%
$82$
0%
$76$
0%
$14$

Explanation

$\sqrt{1764} =\sqrt{ \underline{2 \times 2} \times \underline{3\times 3} \times \underline{7 \times 7}}$

$=2\times 3\times 7$

$=42$

What should be multiplied to

$7200$ to make a perfect square?

0%
$5$
0%
$3$
0%
$2$
0%
$4$

Use prime factorisation to find the square root of

$1225$ .

0%
$122$
0%
$225$
0%
$35$
0%
$50$

Explanation

$1225 = 5 \times 5 \times 7 \times 7= 35 \times 35$

$\sqrt{1225} =\sqrt{ 5 \times 5 \times 7 \times 7}=5\times 7= 35$

Find perfect square numbers between

$50$ and

$60$ .

0%
$50$ , $54$
0%
$52$ , $58$
0%
$56$ , $59$
0%
None of the above

Explanation

By squaring, we get as

$1$

$\rightarrow$

$1$

$2$

$\rightarrow$

$4$

$3$

$\rightarrow$

$9$

$4$

$\rightarrow$

$16$

$5$

$\rightarrow$

$25$

$6$

$\rightarrow$

$36$

$7$

$\rightarrow$

$49$

$8$

$\rightarrow$

$64$

From, this we can say that there is no perfect square between

$50$ and

$60$ .

Which smaller number should be used to divide

$3650$ to get a perfect square?

0%
$142$
0%
$152$
0%
$146$
0%
$154$

Explanation

$3650 = 2 \times \underline{5 \times 5} \times 73$
To get a perfect square we have to divide

$3650$ by

$2 \times 73 = 146$ .

$3650\div 146 = 25$

The square root of

$625$ is:

0%
$62$
0%
$25$
0%
$12$
0%
$66$

Explanation

$\textbf{Step -1: Find prime factors of 625.}$

$\text{Prime factors of }625=5\times5\times5\times5.$

$\textbf{Step -2: Find the square root of 625.}$

$\sqrt{625}=\sqrt{5\times5\times5\times5}$

$=5\times5$

$=25$

$\textbf{Hence, B is the correct option.}$

The area of stadium which is in the shape of square is

$2401$ . Find the side of a square plot.

0%
$89$
0%
$42$
0%
$49$
0%
$16$

Explanation

Area of square is (side)

$^2$

Since, side

$^2$

$=2401$

Therefore, side

$=\sqrt{2401}=\sqrt{7\times7\times7\times 7}=7\times 7=49$

Evaluate

$\sqrt {42.25}$ .

0%
$7.5$
0%
$9.1$
0%
$21.25$
0%
$6.5$

Mr. Hansraj wants to find the least number of boxes to be added to get a perfect square. He already has

$7924$ boxes with him. How many more boxes are required?

0%
$819$
0%
$412$
0%
$419$
0%
$176$

Explanation

Find square root by long division method.

$\therefore \sqrt {7924}$ =

$89.01$

Hence, the perfect square number smaller than

$7924$ is

$89^2 = 7921$

The next perfect square no. is

$90^2 = 8100$

So,

$8100 - 7924 = 176$

Therefore, the man needs

$176$ more boxes in order to get a perfect square number.

So, option D is correct.

Use division method to get the square root of

$5041$ .

0%
$51$
0%
$41$
0%
$31$
0%
$71$

Explanation

$\therefore \sqrt{5041} = 71$

CBSE Questions for Class 8 Maths Squares And Square Roots Quiz 6 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

CBSE Questions for Class 8 Maths Squares And Square Roots Quiz 6 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

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