List of top Mathematics Questions on Square Roots

The sum of squares of roots of $ |x - 2|^2 - |x - 2| - 2 = 0 $ and $ x^2 - 2|x - 3| - 5 = 0 $ equals to:

The value of \( \frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}} \) is:

If the equation \(3x^2 – 10x + 2p\) = 0 has equal roots then the value of p is –

If x=1 is a common root of ax²+ax+2=0 and x²+x+b=0, then the value of ab is

\(\sqrt{3}x + \sqrt{2}y = 2\sqrt{2}\) ; \(\sqrt{2}x - \sqrt{3}y = 3\sqrt{3}\) implies \(x=,y=\)

The roots of \(2x-\frac{2}{x}= 3\) are 

For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained. 

1. 252 
2. 2925 
3. 396 
4. 2645 
5. 2800 
6.  1620

For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. 

1. 252 
2.  180 
3.  1008 
4.  2028 
5.  1458 
6.  768

Find the square roots of the following numbers by the Prime Factorisation Method. 

1. 729 
2. 400 
3.  1764 
4.  4096 
5.  7744 
6.  9604 
7.  5929 
8.  9216 
9.  529 
10.  8100

Find the smallest square number that is divisible by each of the numbers \(8, 15\), and \(20\).

Find the smallest square number that is divisible by each of the numbers \(4, 9\), and \(10\).

\(2025\) plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

The students of Class VIII of a school donated Rs \(2401\) in all, for Prime Minister's National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.

Find the square roots of \(100\) and \(169\) by the method of repeated subtraction.

Without doing any calculation, find the numbers which are surely not perfect squares. 

1. 153 
2. 257 
3. 408 
4. 441

What could be the possible 'one's' digits of the square root of each of the following numbers? 

1. 9801 
2. 99856 
3. 998001 
4. 657666025