# Free Squares and Square Roots 03 Practice Test - 8th Grade

What will be the number of zeroes in the square of 60?

A. 2
B. 1
C. 3
D. 4

#### SOLUTION

Solution : A

If a number ends with n zeroes, its square will end with 2n zeroes.

Here, 60 ends with one zero, so its square will end with 2 zeroes.

It is important to note that this stands true only for natural numbers (not decimals).

Which of the following could be a perfect square?

A.

1681

B.

23453

C.

222222

D.

1057

#### SOLUTION

Solution : A

Perfect squares cannot have 2, 3, 7 or 8 in their unit's place.
In the given options only 1681 does not end with a number other than these.

The perfect squares of numbers ending in 1 and 9 have 1 at their unit's place.

Thus, 1681 could be a perfect square of an integer ending with either 1 or 9.

Which of the following will have 1 in its unit's place?

A.

1232

B.

1612

C.

822

D.

772

#### SOLUTION

Solution : B

The square of a number will end in 1, if the digit in the units place is either 1 or 9 .
We know that 12=1 and 92=81.

Among the given options, 161 has 1 in its units place.

Hence, (161)2 will have 1 in its units place.

If A, B, C, ..., X, Y, Z represents digits, which of the following could be a perfect square?

A.

XX1

B.

ABC2

C.

PQR7

D.

Can't be said without actual calculation

#### SOLUTION

Solution : A

The numbers 7, 2 and 3 do not appear in the unit place of any perfect square. So, ABC2 and PQR7 can not be perfect squares and XX1 is the only number which could be a perfect square.

Simplify
81

A.

27

B.

3

C.

9

D.

Can't be determined

#### SOLUTION

Solution : B

81
=(9×9)        [9×9=92=81]
=(9)                  [92=9]=(3×3)           [3×3=32=9]=3

A division is the inverse operation of a square.

A. True
B. False

#### SOLUTION

Solution : B

The square root is the inverse operation of a square.

A division is the inverse operation of multiplication, not of a square.

Square of a perfect cube is another perfect cube.

A. True
B. False

#### SOLUTION

Solution : A

Square of a perfect cube is another perfect cube.
Let us take a number, n.

Its cube is n3. Square of this cube would be a perfect square given by (n3)2, which can also be written as (n2)3, a perfect cube.

Square root of 1024 is 32.

A. True
B. False

#### SOLUTION

Solution : A

By division method,
3  23¯¯¯¯¯¯10 ¯¯¯¯¯¯249 62   124   124   0

The square root of 1024 is 32.

Which of the following are perfect squares?

A. 156
B.

176

C. 196
D. 256

#### SOLUTION

Solution : C and D

The square root of a perfect square is a natural number.
196  =  14×14  =  14

256  =  16×16  =  16

Whereas 156 and 176 are not the perfect squares.
Hence, 196 and 256 are perfect squares as they are squares of 14 and 16 respectively.

There is/are ___ perfect square/squares between 50 and 70.

#### SOLUTION

Solution :

64 is the square of 8 which lies between 50 and 70. The squares of 7 and 9 are 49 and 81 respectively which lie outside this range. Therefore there is one perfect square between 50 and 70.