Squares and Square Roots Test

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Squares and Square Roots Test - 12

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Weekly Quiz Competition

Question 1
1 / -0

All perfect squares end in 0, 1, 4, 5, 6, __.

A
3

B
2

C
9

D
7

Solution

All perfect squares end in $$0, 1, 4, 5, 6, 9$$.
Example: $$484, 169, 625, 100, 676, 121$$ are perfect squares.
Question 2
1 / -0

Identify the Pythagorean triplet.

A
$$\left( 6,8,10 \right) $$

B
$$\left( 3,4,7 \right) $$

C
$$\left( 5,12,18 \right) $$

D
$$\left( 2,3,6 \right) $$

Solution

A pythagorean triplet satisfies
$${ c }^{ 2 }={ a }^{ 2 }+{ b }^{ 2 }$$

In the option $$A,$$
Let $$c=10, \ a=6,\ b=8.$$
So,
$${ c }^{ 2 }={ (10) }^{ 2 }$$
$$=100$$

And,
$$ { a }^{ 2 }+{ b }^{ 2 }={ 6 }^{ 2 }+{ 8 }^{ 2 }$$
$$=36+64$$
$$=100$$

$$ \Rightarrow { c }^{ 2 }={ a }^{ 2 }+{ b }^{ 2 }$$

So $$(6,8,10)$$ is Pythagorean triplet.
The triplets in the rest of the options do not satisfy the above condition.
Question 3
1 / -0

How many two-digit numbers satisfy this property: The last digit (unit's digit) of the square of the two-digit number is 8 ?

A
1

B
2

C
3

D
None of these

Solution

As we know that all the perfect square number ends with $$1,4,9,6,5,00$$
So, a number ending in 8 can never be a perfect square.
Question 4
1 / -0

Which one of the following can't be the square of natural number?

A
$$30976$$

B
$$75625$$

C
$$28561$$

D
$$143642$$

E
None of these

Solution

The square of a natural number never ends with $$2$$ as the unit's digit.
$$\therefore$$ $$143642$$ is not the square of natural number because it has 2 as the unit's digit.
Question 5
1 / -0

A man plants his orchard with $$5625$$ trees, and arranges them so that there are as many rows as there are trees in a row; how many rows are there?

A
$$65$$

B
$$75$$

C
$$85$$

D
$$55$$

Solution

It simply means that number of trees in a row & in a single coloum is same
Let this be $$x$$ then it will form a square field with side length $$x$$
Hence $$x^2$$ $$= 5625 $$
=> $$x = 75$$
Question 6
1 / -0

What will be the units digit of the square of the given number $$7286$$ ?

A
$$0$$

B
$$1$$

C
$$5$$

D
$$6$$

Solution

Unit digit of multiplication of $$2$$ numbers is obtained by taking the last digit of the multiplication of two numbers i.e. the digits at the unit place
Units digit of $$7286\times 7286$$ is obtained by taking the last digit of $$6\times 6=36$$
$$\Rightarrow $$ Unit digit of square of $$7286$$ is $$6$$.
Question 7
1 / -0

What will be the units digit of the square of the given number $$39$$?

A
$$9$$

B
$$3$$

C
$$1$$

D
$$0$$

Solution

Unit digit of multiplication of 2 numbers is obtained by taking the last digit of the multiplication of two numbers i.e. the digits in the unit place
Units digit of $$39×39$$ is obtained by taking the last digit of $$9×9=81$$
$$\Rightarrow $$ Unit digit of square of $$39$$ is $$1$$.
Question 8
1 / -0

Which of the following is not a perfect square?

A
$$16384$$

B
$$23857$$

C
$$18496$$

D
$$11025$$

Solution

$$16384= 128\times 128$$ (perfect square)
$$18496=136\times 136$$ (perfect square)
$$11025=105\times 105$$ (perfect square)
$$23857 = 1\times 23857$$ (prime no. so not a perfect square)
Hence, option B is correct.
Question 9
1 / -0

Which one of the following numbers is not a perfect square from $$4900, 90000, 810000, 81000$$?

A
$$4900$$

B
$$90000$$

C
$$810000$$

D
$$81000$$

Solution

$$\sqrt { 4900 } =70$$ perfect square
$$\sqrt { 90000 } =300$$ perfect square
$$\sqrt { 810000 } =900$$ perfect square
$$\sqrt { 81000 } $$ is not an integer
$$\sqrt { 81000 } $$ is not a perfect square
Question 10
1 / -0

Find the value of $$5^2$$.

A
20

B
25

C
22

D
5

Solution

$$\textbf{Step-1: Finding }$$ $$5^2$$
$${5^2= }$$ $$ 5\times 5 = $$ $$25$$
$$\textbf{Hence,}$$ $$ 5\times 5 = $$ $$25$$

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Re-Attempt Weekly Quiz Competition

Squares and Square Roots Test - 12

Result

Squares and Square Roots Test - 12

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SHARING IS CARING

Question 1

3

2

9

7

Solution

Question 2

$$\left( 6,8,10 \right) $$

$$\left( 3,4,7 \right) $$

$$\left( 5,12,18 \right) $$

$$\left( 2,3,6 \right) $$

Solution

Question 3

1

2

3

None of these

Solution

Question 4

$$30976$$

$$75625$$

$$28561$$

$$143642$$

None of these

Solution

Question 5

$$65$$

$$75$$

$$85$$

$$55$$

Solution

Question 6

$$0$$

$$1$$

$$5$$

$$6$$

Solution

Question 7

$$9$$

$$3$$

$$1$$

$$0$$

Solution

Question 8

$$16384$$

$$23857$$

$$18496$$

$$11025$$

Solution

Question 9

$$4900$$

$$90000$$

$$810000$$

$$81000$$

Solution

Question 10

20

25

22

5

Solution

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