Square and Square Roots Class 8 Questions

Square and Square Roots Class 8 Questions, deals with various types of questions which are as under:-

Finding the perfect square
Finding the number to be multiplied to make perfect square
Finding the square of two-digit number
Finding the value of expression using identity
Finding the value of square root term
Finding the value of unknown term using identity
Word problems on Square root

Square and Square Roots Class 8 Questions – Finding the perfect square

Question 1:

Which one of the following is perfect square ?

488 , 732 , 121, 3482

Solution:

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

Since, 488 , 732 and 3482 end with 8 , 2, 2 , therefore, they cannot be perfect square.

But, 121 can be written as

121 = 11 x 11

Hence, 121 is a perfect square.

Square and Square Roots Class 8 Questions – Finding the number to be multiplied to make perfect square

Question 2:

What is the least number by which 450 should be multiplied, so that the product of the two numbers would be a perfect square?

Solution:

If we find the factors of 450 , we would get 450 = 3 x 3 x 5 x 5 x 2

If we draw out the factors in pairs, we would notice that we have pairs of 3 and 5 , but 2 is the only single number, which is not in pair.

Therefore if 450 is multiplied by 2 then the product would be a complete square.

Square and Square Roots Class 8 Questions – Finding the square of two digit number

Question 3:

What is the value of $\left(91 \right) ^{ 2 }$

Solution:

We know that ${ (a-b) }^{ 2 }\quad =\quad { a }^{ 2 }\quad +\quad { b }^{ 2 }\quad -\quad 2ab$

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 91 as ( 100 – 9 )

$91^{ 2 }$ = $\left(100-9 \right) ^{2 }$

Applying ${ (a-b) }^{ 2 }\quad =\quad { a }^{ 2 }\quad +\quad { b }^{ 2 }\quad -\quad 2ab$ and substituting the value of a and b, we get

= $\left(100 \right) ^{ 2 }$ + $9^{2}$ – 2 x 100 x 9

= 10000 + 81 – 1800

= 10081 – 1800

= 8281

Square and Square Roots Class 8 Questions – Finding the value of expression using identity

Question 4:

$\cfrac {22\times 22-2\times 20\times 22+20\times 20 }{ \left( 2 \right) ^{ 2 } }$ = ?

Solution:

We know that ${ (a-b) }^{ 2 }\quad =\quad { a }^{ 2 }\quad -\quad 2ab\quad +\quad { b }^{ 2 }\quad$

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

= $22^{ 2 }-2\times 20\times 22+20^{ 2 }$

Or we can say that the given equation has value of

a = 22 and b = 20

So we can replace the numeration

22 x 22 – 2 x 20 x 22 + 20 x 20 with $\left( 22-20 \right) ^{ 2 }=\left( 2 \right) ^{ 2 }$

Now putting these values in Numerator, we would get

$\cfrac {2^{ 2 } }{ 2^{ 2 } }$ = $\cfrac {4}{4}$ = 1

Question 5:

Find the value of $\left(44 \right) ^{ 2 }-\left(43 \right) ^{ 2 }+2^{2}$

Solution:

$\left(44 \right) ^{ 2 }-\left(43 \right) ^{ 2 }+2^{2}$

We know that $\left( a^{ 2 }-b^{ 2 } \right) =\left( a-b \right) \left( a+b \right)$

a = 44 and b = 43

= ( 44 + 43 ) ( 44 – 43 ) + 4

= 87 x 1 + 4

= 87 + 4

= 91

Question 6:

The value of $\left(555 \right) ^{ 2 }$ – $\left(554 \right) ^{ 2 }$ ?

Solution:

We know that $\left( a \right) ^{ 2 }-\left( b \right) ^{ 2 }=\left( a-b \right) \left( a+b \right)$

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

a = 555 and b = 554

So we can rewrite the above equation as

$555^{2 }-554^{2 }$ = ( 555 + 554 ) ( 555 – 554 )

= 1109 x 1

= 1109

Square and Square Roots Class 8 Questions – Finding the value of square root term

Question 7:

If $\sqrt {18 }$ = 4.24 , what is the value of $\sqrt { \cfrac {2 }{ 9} }$ ?

Solution:

In order to solve these type of problems, we first need to equate the value which has to be solved $\sqrt { \cfrac {2 }{ 9} }$ of the given equation in the given equation

We can write $\sqrt {18}$ = 4.24

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

$\sqrt { \cfrac { 2\times 9 }{ 9\times 9 }}$

= $\sqrt { \cfrac {18}{81} }$

= $\cfrac { \sqrt {18 } }{9}$

= $\cfrac {4.24}{9}$

= 0.47

Square and Square Roots Class 8 Questions – Finding the value of unknown term using identity

Question 8:

If $42^{2}$ – $40^{2}$ = { $\left(12 \right) ^{ 2 }$ – $\left(10 \right) ^{ 2 }$ } x Y , then the value of Y is ?

Solution:

Since,

$\left( a^{ 2 }-b^{ 2 } \right) =\left( a-b \right) \left( a+b \right)$

We can rewrite both the equation as

$42^{2}$ – $40^{2}$ = { $\left(12 \right) ^{ 2 }$ – $\left(10 \right) ^{ 2 }$ } x Y

( 42 + 40 ) x ( 42 – 40 ) = ( 12 + 10 ) x ( 12 – 10 ) x Y

82 x 2 = 22 x 2 x Y

164 = 44 x Y

Or,

Y = $\cfrac {164}{44}$

Y = $\cfrac {41}{11}$

Square and Square Roots Class 8 Questions – Word problems on Square root

Question 9:

In a conference hall of a school, 900 students were sitting in such a way that there were as many rows as there were students in a row. How many rows were there?

Solution:

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

$x\times x$ =900,

$x^{ 2 }$ =900

x=√900

= √ 3 x 3 x 5 x 5 x 2 x 2

= 3 x 5 x 2

= 30

Hence, the number of rows = Number of students in a row = 30

Question 10:

A group of People decided to collect as many paisa from each member of the group as is the number of members. If the total collection amounts to Rs. 11.56 , the number of members in the group is ?

Solution:

Funds collected in paisa= 11.56 x 100

= 1156

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

1156= Numbers of the members of the group x Paisa collected from each memeber

Let the Number of members of the group= $x$

Then Paisa collected from each member= $x$

Substituting these values in the given equation

1156= $x$ x $x$ ,

$x^{ 2 }$ = 1156

Or,

$x$ = $\sqrt {1156}$ ,

$x$ = 34

Numbers of the members of the group = 34

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Square and Square Roots Class 8 Questions

Square and Square Roots Class 8 Questions – Finding the perfect square

Square and Square Roots Class 8 Questions – Finding the number to be multiplied to make perfect square

Square and Square Roots Class 8 Questions – Finding the square of two digit number

Square and Square Roots Class 8 Questions – Finding the value of expression using identity

Square and Square Roots Class 8 Questions – Finding the value of square root term

Square and Square Roots Class 8 Questions – Finding the value of unknown term using identity

Square and Square Roots Class 8 Questions – Word problems on Square root

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Square and Square Roots Class 8 Questions – Finding the perfect square

Square and Square Roots Class 8 Questions – Finding the number to be multiplied to make perfect square

Square and Square Roots Class 8 Questions – Finding the square of two digit number

Square and Square Roots Class 8 Questions – Finding the value of expression using identity

Square and Square Roots Class 8 Questions – Finding the value of square root term

Square and Square Roots Class 8 Questions – Finding the value of unknown term using identity

Square and Square Roots Class 8 Questions – Word problems on Square root

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