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

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(a) 5650

(b) 6650

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

(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, “5” remains without pair.
• Therefore, smallest number that must be multiplied or divided by to make 8820 perfect square is “5” .

• 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, “” remains without pair.
• Therefore, smallest number that must be multiplied or divided by to make 8400 perfect square is “21” .

• 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, “” remains without pair.
• So smallest number that must be multiplied or divided by to make 6500 perfect square is “65” .

• 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, “” remains without pair.
• So smallest number that must be multiplied or divided by to make 4536 perfect square is “14” .

• 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 “6” by itself by “0” time
• So,

• 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. () .
• So, Square root of is

• 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. () .
• So, Square root of is

• 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

• 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

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

• 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 () .
• So, square root of 0.053 in two digit is 0.23

• 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 () .

• Now, Square root of 536 using long division method is given below,
• So,
• Square root of 248 using long division method is given below,
• So,
• Now,