Squares and Square Roots Test

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Squares and Square Roots Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

Find the square root correct upto $$2$$ decimals $$60.92$$.

A
$$7.92$$

B
$$7.81$$

C
$$7.27$$

D
$$7.56$$

Solution

$$\sqrt{6092}$$

$$=\sqrt{\dfrac{6092}{100}}$$

$$=\dfrac{78.05}{10}$$

$$=7.81$$
Question 2
1 / -0

The smallest four digit number which is perfect square is ____.

A
$$1000$$

B
$$1016$$

C
$$1024$$

D
$$1036$$

Solution

Consider,
$$31\times 31=961$$
$$32\times 32=1024$$
$$\therefore$$ Smallest four-digit number which is perfect square is $$1024$$.
Question 3
1 / -0

Which of the following will have $$4$$ at the units place?

A
$$(14)^2$$

B
$$(62)^2$$

C
$$(27)^2$$

D
$$(35)^2$$

Solution

Unit digit of $$62 $$ is $$2$$ and the square of $$2$$ is $$ 4$$.
Question 4
1 / -0

If $$\frac{18\times 72\times x}{48\times 315} = \sqrt{81}$$, then $$x = \underline{ }$$

A
115

B
150

C
15

D
105

Solution
Question 5
1 / -0

There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement?

A
16

B
20

C
25

D
32

Solution

Total number of children in a school = $$500$$
For P.T. Drill number of rows = number of columns =$$ x$$
The number of children who will be left out = $$500 - x^2$$. The square root of $$500$$ gives remainder as 16 that means, the square of $$22$$ is less than $$500$$ by $$16$$
To make it a perfect square = $$500-16 = 484$$
Therefore, number of children left will be $$16$$
Question 6
1 / -0

The square root of 350 lies between which pair of numbers?

A
18 and 19

B
35 and 36

C
3.5 and 3.6

D
7 and 8
Question 7
1 / -0

The least number which is a perfect square and has $$540$$ as a factor is

A
$$8,100$$

B
$$6,400$$

C
$$4,900$$

D
$$3,600$$

Solution

The number must be a product of $$540$$ and another number.
$$540 = 9\times 4\times 15$$
Now, the least number to be multiplied with $$540$$ is $$15$$ to make it a perfect square.
So, the required number is $$540\times 15 = 8100$$
Question 8
1 / -0

Pythagorean triplet of given number $$6$$ is

A
$$6, 8, 10$$

B
$$6, 9, 10$$

C
$$6, 8, 11$$

D
$$6, 7, 10$$

Solution

$$2k$$, $$(k^2 + 1)$$ and $$(k^2 - 1)$$ form a Pythagorean triplet for any number, k > 1

Let $$2k = 6$$
Hence, $$k = 3$$

and, $$k^2 + 1 = 3^2 + 1= 9 + 1 = 10$$
and, $$k^2 - 1 = 3^2 - 1 = 9 - 1 = 8$$

Check the answers: $$6^2 + 8^2 = 36 + 64 = 100 = 10^2$$

Hence, the triplet is $$ 6, 8,10$$
Question 9
1 / -0

By splitting into prime factors, find the square root of $$729$$.

A
$$27$$

B
$$21$$

C
$$17$$

D
$$87$$

Solution

Prime factorisation of $$729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3$$
$$\sqrt{729} = \sqrt{3 \times 3\times 3\times 3 \times 3\times 3} = 3 \times 3\times 3 = 27 $$
Question 10
1 / -0

By splitting into prime factors, find the square root of $$11025$$.

A
$$1005$$

B
$$105$$

C
$$100$$

D
$$115$$

Solution

Prime factorisation of $$ 11025 = {5} ^{2} \times { 3 } ^ {2} \times { 7 } ^ {2} $$
$$ \sqrt {11025} = \sqrt {{5} ^{2} \times { 3 } ^ {2} \times { 7 } ^ {2}} = 5 \times 3 \times 7= 105 $$.

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Re-Attempt Weekly Quiz Competition

Squares and Square Roots Test - 13

Result

Squares and Square Roots Test - 13

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SHARING IS CARING

Question 1

$$7.92$$

$$7.81$$

$$7.27$$

$$7.56$$

Solution

Question 2

$$1000$$

$$1016$$

$$1024$$

$$1036$$

Solution

Question 3

$$(14)^2$$

$$(62)^2$$

$$(27)^2$$

$$(35)^2$$

Solution

Question 4

115

150

15

105

Solution

Question 5

16

20

25

32

Solution

Question 6

18 and 19

35 and 36

3.5 and 3.6

7 and 8

Question 7

$$8,100$$

$$6,400$$

$$4,900$$

$$3,600$$

Solution

Question 8

$$6, 8, 10$$

$$6, 9, 10$$

$$6, 8, 11$$

$$6, 7, 10$$

Solution

Question 9

$$27$$

$$21$$

$$17$$

$$87$$

Solution

Question 10

$$1005$$

$$105$$

$$100$$

$$115$$

Solution

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