Simplify: 0 . 441 0 . 625

We know, To find the square root of a rational number, If a , b are any two whole numbers, b ≠ 0 , then a b = a b . Now, Start finding the square root by long division process as done for natural number. Stop the process when the remainder is zero. The quotient so obtained is the required square root. Given, 0 . 441 0 . 625 ⇒ 441 1000 625 1000 ⇒ 441 625 Therefore, we get: 2 1 2 4 , 4 1 4 41 0 4 1 4 1 0 and 2 5 2 6 , 2 5 4 45 2 2 5 2 2 5 0 Hence, simplified form of 0 . 441 0 . 625 is 21 25 .

The area of a square field is 101 1 400 m 2 . Find the length of the one side of the field.

Given, Area of the square field = 101 1 400 m 2 = 40401 400 m 2 We know, Area of square = side 2 Therefore, we get: ⇒ side 2 = 40401 400 m 2 ⇒ side = 40401 400 = 40401 400 2 0 1 2 4 , 0 4 , 0 1 4 401 0 0 4 0 1 4 0 1 0 and 400 = 20 That is, side = 201 20 m = 10 1 20 m Hence, the required answer is 10 1 20 m .

Find the square root of 52 857 2116

We know, To find the square root of a rational number, If a , b are any two whole numbers, b ≠ 0 , then a b = a b . Now, Start finding the square root by long division process as done for natural number. Stop the process when the remainder is zero. The quotient so obtained is the required square root. Given, 52 857 2116 ⇒ 52 857 2116 = 110889 2116 Therefore, we get: 3 3 3 3 1 1 , 0 8 , 8 9 9 63 2 0 8 1 8 9 663 1 9 8 9 1 9 8 9 0 4 6 4 2 1 , 1 6 1 6 86 5 1 6 5 1 6 0 Hence, 52 857 2116 = 333 46 .

Find the value of 243 867

We know, To find the square root of a rational number, If a , b are any two whole numbers, b ≠ 0 , then a b = a b . Now, Start finding the square root by prime factorisation method as done for natural number. Stop the process when the remainder is zero. Take one out of each pair and multiply to get the square root. Given, 243 867 ⇒ 243 867 = 243 867 Therefore, we get: 3 2 4 3 3 8 1 3 2 7 3 9 3 and 3 8 6 7 17 2 8 9 17 243 867 = 3 × 3 × 3 3 × 17 = 9 17 Hence, 243 867 = 9 17 .

Find the value of 0 . 0196

We know, To find the square root of a decimal number, Convert it to rational number first. If a , b are any two whole numbers, b ≠ 0 , then a b = a b . Now, Start finding the square root by long division process as done for natural number. Stop the process when the remainder is zero. The quotient so obtained is the required square root. Given, 0 . 0196 ⇒ 0 . 0196 = 196 10000 Therefore, we get: 1 4 1 1 , 9 6 1 24 0 9 6 9 6 0 and 10000 = 100 196 10000 = 14 100 = 0 . 14 Hence, the value of 0 . 0196 is 0 . 14 .

Find the value of 37 . 0881

We know, To find the square root of a decimal number, Convert it to rational number first. If a , b are any two whole numbers, b ≠ 0 , then a b = a b . Now, Start finding the square root by long division process as done for natural number. Stop the process when the remainder is zero. The quotient so obtained is the required square root. Given, 37 . 0881 ⇒ 37 . 0881 = 370881 10000 Therefore, we get: 6 0 9 6 3 7 , 0 8 , 8 1 3 6 1209 1 0 8 8 1 1 0 8 8 1 0 and 10000 = 100 370881 10000 = 609 100 = 6 . 09 Hence, the value of 37 . 0881 is 6 . 09 .

Evaluate 50625 and using its value, calculate 506 . 25 + 5 . 0625 .

Given, To calculate: 506 . 25 + 5 . 0625 . Therefore, we get: 2 2 5 2 5 , 0 6 , 2 5 4 42 1 0 6 8 4 445 2 2 2 5 2 2 2 5 0 50625 = 225 We can write the given decimals in rational form. That is, 506 . 25 = 50625 100 and 5 . 0625 = 50625 10000 Thus, we get: 506 . 25 + 5 . 0625 = 50625 100 + 50625 10000 = 225 10 + 225 100 = 22 . 5 + 2 . 25 = 24 . 75 Hence, the required answer is 24 . 75 .

E M B I B E

Maths Hub (ICSE)>Chapter 3 - Squares and Square Roots>CHECK POINT

S Purkayastha Solutions for Chapter: Squares and Square Roots, Exercise 6: CHECK POINT

Author:S Purkayastha

S Purkayastha Mathematics Solutions for Exercise - S Purkayastha Solutions for Chapter: Squares and Square Roots, Exercise 6: CHECK POINT

Attempt the free practice questions on Chapter 3: Squares and Square Roots, Exercise 6: CHECK POINT with hints and solutions to strengthen your understanding. Maths Hub (ICSE) solutions are prepared by Experienced Embibe Experts.