Properties of Square Numbers

Q.

Find the smallest perfect square divisible by 3, 4 5 and 6.

1. 441

2. 257

3. 153

4. 408

Q.

Which of the following numbers is a square as well as a triangular number?

1. 6

2. 1

3. 28

4. 10

Q.

Question 1 (ii)
What will be the unit digit of the squares of the following number:

272

Q. How many numbers lie between squares of 99 and 100?

Q.

What will be the unit digit of the squares of the following numbers?

$1234$

Q.

Find the square root of $256$

Q.

Find the square root of $2401$ with prime factorization.

Q.

Let $z=x+iy$ be a non-zero complex number such that $z^2=i|z{|}^2$, where$i=\sqrt{-1}$ , then $z$ lies on the

1. line, $y=x$

2. Real axis

3. Imaginary axis

4. line, $y=-x$

Q. Write (T) for true and (F) for false foe each of the statements given below:
(i) The number of digits in a perfect square is even.
(ii) The square of a prime number is prime.
(iii) The sum of two perfect square is a perfect square.
(iv) The difference of two perfect squares is a perfect square.
(v) The product of two perfect squares in a perfect square.

Q.

Give a reason to show that none of the numbers given below is perfect square:
(i) 5372
(ii) 5963
(iii) 8457
(iv) 9468
(v) 360
(vi) 6400
(vii) 2500000

Q.

How many perfect squares are between 100 and 200?

Q.

How to find the square roots of a five digit number 16244

Q.

The number of complex numbers $z$ such that $\left|z-1\right|=\left|z+1\right|=\left|z-i\right|$ equal

1. $0$

2. $1$

3. $2$

4. Infinity

Q.

Write all the three digits numbers using the digits $2,3,5$ taking each digit only once.

Q.

Which of the following are squares of odd numbers?
(i) 484
(ii) 961
(iii) 7396
(iv) 8649
(v) 4225

Q. A perfect square number having n digits , where n is even will have square root with _____.

1. $\left(\sqrt{n}\right)$digit/digits
2. $(n+1)$digit/digits
3. $\left(\frac{n}{2}\right)$digit/digits
4. $\left(\frac{n}{3}\right)$digit/digits

Q.

The square of which of the following would be an odd number?

1. 434

2. 2826

3. 7779

4. 82004

Q.

Find the square root of $256$ by prime factorization method

Q. What is the square of 55?

1. 2025
2. 3035
3. 3025
4. 1025

Q. The sum of two consecutive triangular numbers gives a square number.

1. True
2. False

Q.

Show that the following numbers are not perfect squares:
(i) 9327 (ii) 4058
(iii) 22453 (iv) 743522

Q.

Using the prime factorization method, find $6859$is a perfect cube or not.

Q.

Find the square root of $2304$ by prime factorization method.

Q.

Which of the following are squares of even numbers?
(i) 196
(ii) 441
(iii) 900
(iv) 625
(v) 324

Q.

How many non-perfect square numbers lie between the squares of 3 and 4?

1. 4

2. 6

3. 5

4. 7

Q.

The following numbers are not perfect squares . Give reason :
(i) 1547 (ii) 45743
(iii) 8948 (iv) 333333

Q.

By just examining the units digits , can you tell which of the following cannot be whole squares ?
(i) 1026 (ii) 1028
(iii) 1024 (iv) 1022
(v) 1023 (vi) 1027

Q.

What will be the units digit of the squares of the following numbers?
(i) 52 (ii) 977
(iii) 4583 (iv) 78367
(v) 52698 (vi) 99880
(vii) 12796 (viii) 55555
(ix) 53924

Q.

What will be the unit digit of the square of 27?

1. 9

2. 5

3. 7

4. 1

Q.

How many non-perfect square numbers lie between squares of the following numbers:

A) 14and15

B) 90 and 91