WORKSHEET ON SQUARE ROOT USING PRIME FACTORIZATION METHOD

Practice problems on squares and square root

Problem 1 :

196 is the square of

(A)  11     (B)  12     (C)  14     (D)  16

Solution

Problem 2 :

Which of the following is a square of an even number ?

(A)  144     (B)  169     (C)  441     (D)  625

Solution

Problem 3 :

The square root of 1521 is 31 ?

(A)  True     (B)  False     (C)  None of these

Solution

Problem 4 :

The square of 2.8 is 78.4 ?

(A)  True     (B)  False     (C)  None of these

Solution

Problem 5 :

1000 is a perfect square ?

(A)  True     (B)  False     (C)  None of these

Solution

Problem 6 :

Which of the following is a square of an odd number ?

(A)  256     (B)  361     (C)  144     (D)  400

Solution

Problem 7 :

Which of the following is not a perfect square ?

(A)  361     (B)  1156     (C)  1128     (D)  1681

Solution

Problem 8 :

The value of √(176 + √2401)

(A)  14     (B)  15     (C)  16     (D)  17

Solution

Problem 9 :

A perfect square can never have the following digit at ones place.

(A)  1     (B)  6     (C)  5     (D)  3

Solution

Problem 10 :

Which of the following will have 1 at its unit place ? 

(A)  19²     (B)  17²     (C)  18²    (D)  16²

Solution

Problem 11 :

If 19x² = 100² - 90² , then find the value of x

A.10    B. 9     C. 11      D. 12

Solution

Problem 12 :

√(248 + √(51+√169))

Solution

Problem 13 :

a * b * c = [√(a + 2)(b + 3)] / (c + 1)

 then find the value of 6 * 15 * 3

Solution

Problem 14 :

What will come in place of question mark in each of the following questions ?

√(32.4 / ?) = 2

Solution

Word problems on square roots

Problem 1 :

You have a square blanket that has an area of 1600 square inches. What is the length of 1 side of the blanket ?

Solution

Problem 2 :

A square coffee table has an area of 196 square inches. What is the length of one side of the coffee table ?

Solution

Problem 3 :

You have a square flower garden that has an area of 400 square yards. What is the length of one side of the garden ?

Solution

Problem 4 :

A square desktop has an area of 324 square inches. What is the length of one side of the desktop ?

Solution

Problem 5 :

You want to carpet a square room that has an area of 144 square feet. What is the length of one side of the room ?

Solution

Problem 6 :

You are going to decorate one wall of your bedroom  by putting border along the top. The wall is a square wall with an area of 256 square feet. What is the length of  border you need for the top of this on wall ?

Solution

Problem 7 :

To the nearest tenth, what is the square root of 33 ?

Solution

Problem 8 :

The area of a square tile is 50 square centimeters. To the nearest tenth of a centimeter, how long is one side of this tile ?

Solution

Problem 9 :

Jason's square bedroom has an area of 90 square feet. The length of one side of his room is between what two whole numbers ?

Solution

Problem 10 :

Grandma's square garden has an area of 90 square feet. The length of one side of her garden would be between what two whole numbers ? What is the length of this side to the nearest tenth of a foot ?

Solution

(1)  √289         Solution

(2)  √441      Solution

(3)  √625          Solution

(4)  √1024       Solution

(5)  √0        Solution

(6)  √1369        Solution

(7)  √6889        Solution

(8)  √10000         Solution

(9)   ³√1        Solution

(10)  ³√64           Solution

(11)  ³√125      Solution

(12)  ³√343           Solution

(13)  ⁴√0       Solution

(14)   ⁴√16        Solution

(15)  ³√-1          Solution

(16)  ³√-27        Solution

(17)  ⁴√625        Solution

(18)  ⁵√1        Solution

(19)  ⁵√-1      Solution

(20)  ⁵√-32        Solution

21)  Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.

Solution

22)  Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.

Solution

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