Estimating the Number of Digits in the Square Root of a Number

Q.

Find the smallest square number divisible by each one of the numbers $6$, $9$ and $15$

Q.

Find the smallest square number divisible by each one of the numbers $8,9$ and $10$

Q.

Find the smallest square number divisible by each one of the numbers $4$, $9$ and $10$

Q.

Find the number of digits in the square root of the number $144$

Q.

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

Q.

Without doing any calculation, find the numbers which are surely not perfect squares. $\left(\mathrm{iv}\right)441$

Q.

What is the smallest square number which is divisible by $2,4,5,6$ and $9$?

Q.

Find the smallest square number divisible by each one of the numbers $8,$$15$ and $20$

Q.

How do you simplify the square root of $40$?

Q.

Find the square root of $169$

Q.

Question 21

Write the correct answer from the given four options.

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

a) $(n+1)$ digit
b) $\frac{n}{2}$ digit
c) $\frac{n}{3}$ digit
d) $\left(\frac{n+1}{2}\right)$ digit

Q. How to find square root of any number e.g. 645.

Q.

Find the least square number which is exactly divisible by $3,4,5,6$ and $8$.

Q.

Question 2 (iii)
Find the number of digits in the square root of each of the following numbers (without any calculation):

4489

Q.

How many digits are there in the square root of 758641?

1. 2

2. 3

3. 4

4. 5

Q.

Question 2 (iv)
Find the number of digits in the square root of each of the following numbers (without any calculation):

27225

Q.

What is the square root of 10 rounded to 1 decimal place?

1. 3.2

2. 2.2

3. 3.9

4. 5

Q.

Question 2 (ii)
Find the number of digits in the square root of each of the following numbers (without any calculation):

144

Q. Write the following in symbols:

(1) The positive square root of 400
(2) The negative square root of 81
(3) The negative square root of 121
(4) The positive square root of 1

Q.

What could be the possible One’s digits of the square root of each of the following numbers?

$\left(i\right)9801$

$\left(ii\right)99856$

$\left(iii\right)998001$

$\left(iv\right)657666025$

Q.

A number "p" exists such that it is the square of a number "q". If "p"$>$ 400, "q" can be

1. 15

2. 19

3. 25

4. 29

Q.

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?

1. 27

2. 9

3. 12

4. 81

Q.

Question 72

State whether the following statement is true or false:

The square root of a perfect square of n digits will have $\left(\frac{n+1}{2}\right)$ digits, if n is odd.

Q.

Estimate the square root of 536 to its nearest whole number.

1. 23

2. 24

3. 25

4. 26

Q.

What is the square root of 10 rounded to 1 decimal place?

1. 3.2

2. 2.2

3. 3.9

4. 5

Q.

How many digits will be there before the decimal in the square root of 759589598?

1. 2

2. 3

3. 4

4. 5

Q. Find the number of digits in the square root of the following number (without any calculation).

Q. A rectangle of length and breadth equal to 19 m and 17 m respectively has to be converted into a square of equal area. What will be the approximate length of the side of the square?

1. 16
2. 18
3. 15
4. 20

Q.

Rose remembers that her seat number was not a perfect square and it had repeating digits. Which among the following options is her seat?

1. 77771112
   
2. 44448889
   
3. 7744
   
4. 11115556​​​​​​​
   

Q.

Question 73

State whether the following statement is true or false:

Square root of a number x is denoted by $\sqrt{x}$.