## Square and Square Roots - Worksheet

**Q1**. Find the Pythagorean triplets whose one member is:

a) 8 b) 12

**Q2**. Is 2352 is a perfect square number? If not, find the smallest multiple of 2352 which is a perfect square. Find the square root of the new number.

**Q3**. Find the smallest square number that is divisible by each of the numbers 8, 15, 20.

**Q4**. There are 2401 students in a school P.T. teacher wants them to stand in rows and columns such that number of rows is equal to the number of columns. Find the number of rows.

**Q5**. Find the greatest 4-digit number which is a perfect square.

**Q6**. Find the least number that must be added to 1300 so as to get a perfect square.

**Q7**. Find the least number that must be subtracted from 5607 so as to get a perfect square. Also find the square root of the perfect square.

**Q8**. A gardener has 1000 plants. He has to plant them in such a way that the number of rows and number of columns remain same. Find the minimum number of plant he needs more for this.

**Q9**. Check whether 90 is a perfect square or not by using prime factorisation.

**Q10**. How many natural numbers lie between 5² and 6² ?

**Q11**. Using distributive law, find the square of 43.

**Q12**. Evaluate the square root of 22.09 by long division method.

**Q13**. Find the smallest perfect square divisible by 3, 4, 5 and 6.

**Q14**. Find the length of a diagonal of a rectangle with dimensions 20m by 15m.

**Q15**. During a mass drill exercise, 6250 students of different schools are arranged in rows such that the number of students in each row is equal to the number of rows. In doing so, the instructor finds out that 9 children are left out. Find the number of children in each row of the square.

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