Grade 8 Square and Square Roots Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

Get top class preparation for CBSE/Class-8 right from your home: get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-8.

(1) Each Number Given is a Non-Perfect Square. Find the Smallest Number (N) It Must be Multiplied or Divided by to Make It a Perfect Square

(a)

(b)

(2) Each Number Given is a Non-Perfect Square. Find the Smallest Number (N) It Must be Multiplied or Divided by to Make It a Perfect Square

(a)

(b)

(3) Solve 60

(4) Find the Square Root of 1296 Using the Long-Division Method

(5) Find the Square Root of the 6889 Using the Long-Division Method

(6) Find the Smallest Number (X) Which Must be Added to the Given Number and the Smallest Number Which (Y) Must be Subtracted from the Given Number, So That It Becomes a Perfect Square

(a) 5650

(b) 6650

(7) Evaluate Each of the Following Square-Roots (Rounded off to Three Decimal Places)

(a)

(b)

(8) Simplify

(a)

(9) Approximate the Following Square-Roots to Two Decimal Places Using Long-Division

(a)

(10) Approximate the Following Square-Roots to Two Decimal Places Using Long-Division

(a)

(11) Approximate the Following Square-Roots to Two Decimal Places Using Long-Division

(a)

(12) Approximate the Following Square-Roots to Two Decimal Places Using Long-Division

(a)

Answers and Explanations

Answer 1 (A)

  • Here given number is
  • Now, the perfect square number is number of multiplication of two identical integer number.
  • And to get its roots we have to identify its prime factors.

  • So, Factor of 8820 is
  • Hence, β€œ5” remains without pair.
  • Therefore, smallest number that must be multiplied or divided by to make 8820 perfect square is β€œ5” .

Answer 1 (B)

  • Here given number is
  • Now, the perfect square number is number of multiplication of two identical integer number.
  • And to get its roots we have to identify its prime factors.

  • So, Factor of 8400 is
  • Hence, β€œβ€ remains without pair.
  • Therefore, smallest number that must be multiplied or divided by to make 8400 perfect square is β€œ21” .

Answer 2 (A)

  • Here given number is
  • Now, the perfect square number is number of multiplication of two identical integer number.
  • And to get its roots we have to identify its prime factors.

  • So, Factor of 6500 is
  • So, β€œβ€ remains without pair.
  • So smallest number that must be multiplied or divided by to make 6500 perfect square is β€œ65” .

Answer 2 (B)

  • Here given number is
  • Now, the perfect square number is number of multiplication of two identical integer number.
  • And to get its roots we have to identify its prime factors.

  • So, Factor of 4536 is
  • So, β€œβ€ remains without pair.
  • So smallest number that must be multiplied or divided by to make 4536 perfect square is β€œ14” .

Answer (3)

  • Here given exponents is
  • Exponent to any number means multiplication of number by itself by number of exponent՚s time.
  • So, for multiplication of number β€œ6” by itself by β€œ0” time
  • So,

Answer (4)

  • Step for the long division method to find out square root is as below:
  • Step-1:- Group the digits in pairs, starting with the digit in the units place. So here pairs is
  • Step-2: Think of the largest number whose square is equal to or just less than the first pair (12) , (in our case largest number whose square is equal to or less than 12 is 3 . ()
  • Step-3:- Subtract the product of the divisor (3) and the quotient (3) from the first pair (12) and bring down the next pair (96) to the right of the remainder () . This becomes the new dividend. (
  • Step-4:- Now, the new divisor is obtained by taking two times the quotient () and annexing with it a suitable digit (6) which is also taken as the next digit of the quotient (6) , chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend () .
  • Step-5:- Subtract the product of the divisor (6) and digit (66) from the new dividend. () .
Illustration 2 for Answers_and_Explanations
  • So, Square root of is β€³

Answer (5)

  • Step for the long division method to find out square root is as below:
  • Step-1:- Group the digits in pairs, starting with the digit in the units place. So here pairs is
  • Step-2: Think of the largest number whose square is equal to or just less than the first pair (68) , (in our case largest number whose square is equal to or less than 68 is 8 . ()
  • Step-3:- Subtract the product of the divisor (8) and the quotient (8) from the first pair (68) and bring down the next pair (89) to the right of the remainder (68 ) . This becomes the new dividend. (
  • Step-4:- Now, the new divisor is obtained by taking two times the quotient () and annexing with it a suitable digit (3) which is also taken as the next digit of the quotient (3) , chosen in such a way that the product of the new divisor and this digit is equal to or just less thanthe new dividend () .
  • Step-5:- Subtract the product of the divisor (3) and digit (163) from the new dividend. () .
Illustration 3 for Answers_and_Explanations
  • So, Square root of is β€³

Answer 6 (A)

  • Here given number is
  • Now square root of given number;

  • Square root of given number is 75.17 and it lies between 75 and 76.
  • So, square of;

  • So, smallest number (y) which must be subtract from the given number to make it perfect square is

  • Now, square of ,

  • So, smallest number (x) which must be added to the given number to make it perfect square is

Answer 6 (B)

  • Here given number is
  • Now square root of given number;

  • square root of given number is 81.55 and it lies between 81 and 82.
  • So, square of;

  • So, smallest number (y) which must be subtract from the given number to make it perfect square is

  • Now, square of ,

  • So, smallest number (x) which must be added to the given number to make it perfect square is

Answer 7 (A)

  • Therefore, the answer is

Answer 7 (B)

  • Therefore, the answer is

Answer 8 (A)

  • Here base of exponents is same from right hand side and left hand side,
  • that՚s why we can write as below

Answer 9 (A)

  • Step for the long division method to find out square root of decimal number is as below:
  • Step-1: First we make the pair of the digits of the integral part () and decimal part () by placing the bar of each pair.
  • Step-2: Think of the largest number whose square is equal to or just less than the first pair (0) , (in our case largest number whose square is equal to or less than 0 is 0 . ()
  • Step-3:- Subtract the product of the divisor (0) and the quotient (0) from the first pair (0) and bring down the next pair (05) to the right of the remainder (00 ) . This becomes the new dividend. (
  • Step-4:- Now, the new divisor is obtained by taking two times the quotient () and annexing with it a suitable digit (2) which is also taken as the next digit of the quotient (2) , chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend () .
  • Step-5:- Subtract the product of the divisor (2) and digit (02) from the new dividend. () .
  • Step-6: Bring down the next pair (30) to the right of the remainder () . This becomes the new dividend (130) .
  • Step-7: Now, the new divisor is obtained by taking two times the quotient () and annexing with it a suitable digit (3) which is also taken as the next digit of the quotient (3) , chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend () .
Illustration 4 for Answers_and_Explanations
  • So, square root of 0.053 in two digit is 0.23

Answer 10 (A)

  • Step for the long division method to find out square root of decimal number is as below:
  • Step-1: First we make the pair of the digits of the integral part () and decimal part () by placing the bar of each pair.
  • Step-2: Think of the largest number whose square is equal to or just less than the first pair (0) , (in our case largest number whose square is equal to or less than 0 is 0 . ()
  • Step-3:- Subtract the product of the divisor (0) and the quotient (0) from the first pair (0) and bring down the next pair (00) to the right of the remainder (00 ) . This becomes the new dividend. (
  • Step-4:- Now, the new divisor is obtained by taking two times the quotient () and annexing with it a suitable digit (0) which is also taken as the next digit of the quotient (0) , chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend () .
  • Step-5:- Subtract the product of the divisor (0) and digit (00) from the new dividend. (0 ) .
  • Step-6: Bring down the next pair (56) to the right of the remainder (0) This becomes the new dividend (056) .
  • Step-7: Now, the new divisor is obtained by taking two times the quotient (0 ) and annexing with it a suitable digit (7) which is also taken as the next digit of the quotient (7) , chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend () .
Illustration 5 for Answers_and_Explanations

Answer 11 (A)

  • Now, Square root of 536 using long division method is given below,
Illustration 6 for Answers_and_Explanations
  • So,
  • Square root of 248 using long division method is given below,
Illustration 7 for Answers_and_Explanations
  • So,
  • Now,

Answer 12 (A)

  • Now, Square root of 484 using long division method is given below,
Illustration 8 for Answers_and_Explanations
  • So,
  • Square root of 324 using long division method is given below,
Illustration 9 for Answers_and_Explanations
  • So,
  • Now,

Developed by: