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

### Question 1

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

#### 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).

### Question 2

Which of the following could be a perfect square?

1681

23453

222222

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.

### Question 3

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

1232

1612

822

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.

### Question 4

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

XX1

ABC2

PQR7

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.

### Question 5

Simplify

√√81 =

27

3

9

Can't be determined

#### SOLUTION

Solution :B

√√81

=√(√9×9) [∵9×9=92=81]

=√(9) [∵√92=9]=√(3×3) [∵3×3=32=9]=3

### Question 6

A division is the inverse operation of a square.

#### 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.

### Question 7

Square of a perfect cube is another perfect cube.

#### 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.

### Question 8

Square root of 1024 is 32.

#### SOLUTION

Solution :A

By division method,

3 23¯¯¯¯¯¯10 ¯¯¯¯¯¯249 ↓62 124 124 0

∴ The square root of 1024 is 32.

### Question 9

Which of the following are perfect squares?

176

#### 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.

### Question 10

There is/are

#### 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.