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

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## (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 6^{0}

## (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, β5β remains without pair.
- Therefore, smallest number that must be multiplied or divided by to make 8820 perfect square is
**β5β**.

### 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, ββ remains without pair.
- Therefore, smallest number that must be multiplied or divided by to make 8400 perfect square is
**β21β**.

### 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, ββ remains without pair.
- So smallest number that must be multiplied or divided by to make 6500 perfect square is
**β65β**.

### 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, ββ remains without pair.
- So smallest number that must be multiplied or divided by to make 4536 perfect square is
**β14β**.

### Answer (3)

- Here given exponents is
- Exponent to any number means multiplication of number by itself by number of exponentΥs time.
- So, for multiplication of number β6β by itself by β0β 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. () .

- So, Square root of is β³

### 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. () .

- So, Square root of is β³

### 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,
- thatΥs 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 () .

- 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 () .

### Answer 11 (A)

- 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,

### Answer 12 (A)

- Now, Square root of 484 using long division method is given below,

- So,
- Square root of 324 using long division method is given below,

- So,
- Now,