# Free Squares and Square Roots 01 Practice Test - 8th Grade

Find the square of 39.

A.

78

B.

1500

C.

1521

D.

1530

#### SOLUTION

Solution : C

The number 39 ends with 9.And 92=81 which ends with 1.Hence, 392 should have 1 in the units place.

We can observe from options that only 1521 satisfies this.Hence 1521 is the answer.

Alternatively, 39 should be multiplied with 39 to obtain the square.

So, 39×39=1521.

Find the square of 42.

A.

84

B.

1700

C.

1764

D.

1889

#### SOLUTION

Solution : C

The square of 42 should have 4 in the unit place (since the square of 2 is 4). 84 is too small to be square of 42. So, option 3 is correct.
Alternatively, 42 can be multiplied with itself to give the result.

Aman has 729 coins. He gives only a part of these coins to his cousin as his birthday gift. This part is the square root of 729. How many coins did his cousin get?

A.

27

B.

9

C.

12

D.

81

#### SOLUTION

Solution : A

The square root of 729 should have 3 or 7 in its unit place. Because square of 3 and 7 has 9 in it's units place. Only 27 satisfies this.
Thus, Aman's cousin gets 27 coins as a birthday gift.

Also, we can find the square root using prime factorization as

729=3×3×3×3×3×3

729=36

Square root of 729 is equal to

729=36=33=27

Which among the following are Pythagorean triplets?

A. 15, 8, 17
B. 3, 4, 5
C. 12, 16, 20
D. 1, 1, 2

#### SOLUTION

Solution : A, B, and C

Pythagorean triplets are set of three positive integers a, b, c such that, a2+b2=c2.

152+82=225+64=289=172.Hence, the numbers 15, 8 and 17 form a Pythagorean triplet.

32+42=9+16=25=52.Hence, the numbers 3, 4 and 5 form a Pythagorean triplet.

122+162=144+256=400=202Hence, the numbers 12, 16 and 20form a Pythagorean triplet.

11+11=1+1=222Hence, the numbers 1, 1 and 2does not form a Pythagorean triplet.

Akanksha was asked to multiply a number by its successor. But she was careless and multiplied the number with itself. When she rechecked, she found the error and added the original number to the final result. The result is ___(less/more/equal to) the actual correct answer.

#### SOLUTION

Solution :

Let us express what Akanksha had to do and what she had done, mathematically.

n(n+1)=n2+n

n×n+n=n2+n, which is the same as before.

If a number has 2 or 8 in the unit’s place, then its square ends in

___.

#### SOLUTION

Solution :

22 and 82 always have 4 in the units place. Also, we can see that square of 2 and square of 8 results in 4 and 64 respectively which have 4 in the unit's place.

If 2=1.4142, then the square of 14.142 should approximately be?

A.

20

B.

200

C.

2000

D.

2500

#### SOLUTION

Solution : B

2=1.4142 (Given)

Multiply both sides by 10

10×2=14.142

100×2=14.142

Squaring both sides, we get the square of 14.142  to be approximately equal to 200.

In general, if a natural number m can be expressed as n2, where n is also a natural number, then m is a __________.

A.

perfect square

B.

perfect  cube

C.

perfect number

D.

irrational number

#### SOLUTION

Solution : A

If m can be expressed as n2, where n is a natural number then, m is called a perfect square.

((x2)2)2 = (x3)3

A. True
B. False

#### SOLUTION

Solution : B

((x2)2)2=x8 and (x3)3=x9​
As we can see the square of a square of a square has a total power of 8 whereas the cube of a cube has a total power of 9. Thus, they are not equal.

Numbers like 1, 4, 9, 16, 25, ... are known as ________.

A.

Perfect cubes

B.

Perfect squares

C.

Irrational Numbers

D. Decimals

#### SOLUTION

Solution : B

When an integer is multiplied by itself, it results in a perfect square.

When we square integers like 1, 2, 3, 4, 5, ..., we obtain 1, 4, 9, 16, 25, ... .

Hence, the given numbers which are obtained by squaring the integers are known as perfect squares.