SIMPLIFYING SQUARE ROOTS WORKSHEET

Simplify the following square roots

1)  √36   Solution

2)  √4   Solution

3)  √64    Solution

4)  √144   Solution

5)  -√4    Solution

6)  -√100    Solution

7)  -√1       Solution

8)  -√121    Solution

9)  √-36    Solution

10)  √-9     Solution

11)  √-49    Solution

12)  √(9 + 16)   Solution

13)  √25 + 144    Solution

14)  √9 + √16       Solution

15)  √25 + √144           Solution

Problem 16 :

Find the square root of 6400

Solution

Problem 17 :

Is 2352 a perfect square? If not find the smallest multiple of 2352 which is a perfect square. Find the sqaure root of the new number.

Solution

Problem 18 :

2116 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

Solution

Problem 19 :

A natural number is called a _________ or _____________ if it is the square of some natural numbers 

Solution

Problem 20 :

Simplify √0.09

Solution

Problem 21 :

Find the length of the side of a square whose area is 441 m²

Solution

Simplify the following Radical Expressions

1)  √16x²      Solution

2)  √0.25x^{6    Solution}

3)  √x⁸y^{18    Solution}

4)  √64b^{48     Solution}

5)  -√64a³    Solution

6)  √27y^{6    Solution}

7)  √x⁸y^{12    Solution}

8)  √x^{10    Solution}

9)  √y²         Solution

10)  √b²    Solution

11)  √49x²    Solution

12)  √100y²    Solution

13)  -√64a²    Solution

14)  -√25x²    Solution

15)  √144x²y²    Solution

16)  √196a²b²    Solution

Problem 17 :

Which of the following is equal to x ?

a) x^12/7 - x^5/7      b)  ¹²√ (x⁴)^1/3         c)  (√x²)^2/3     d) x^12/7 ∙ x^7/12

Problem 18 :

Find the value of x in 3 + 2^x = 64^1/2 + 27^1/3

Problem 19 :

If x = (√3 - √2) / (√3 + √2) and y = (√3 + √2) / (√3 - √2) find the value of x² + y² + xy

Problem 20 :

Solve for x in the following questions.

i)  √(32.4/x) = 2      ii)  √86.49 + √(5 + x²) = 12.3

Problem 1 :

The value of √144 + √1.44 is ?

a. 24        b. 13.2       c. 1.32        d. none of these

Solution

Problem 2 :

Which of the following triplet is a Pythagorean Triplet:

a. (4, 5, 6)    b. (11, 60, 61)     c. (10, 8, 6)    d. both b and c

Solution

Problem 3 :

How many non square numbers are there in between 𝑛² 𝑎𝑛𝑑 (𝑛 + 1)²

a. 2n      b. 4n      c. 3n       d. 2n + 1

Solution

Problem 4 :

The Simplified form of 3/√0.09

is

a. 30      b. 3     c. 10       d. None

Solution

Problem 5 :

Evaluate √5² + 12²

Solution

Problem 6 :

2707/√x = 27.07, find x.

Solution

Problem 7 :

If √15625 = 125, then find the value of √156.25 + √1.5625

Solution

Problem 8 :

Find the square root of 14641 by prime factorisation method.

Solution

Problem 9 :

Find the square root of 144 by repeated subtraction method

Solution

Problem 10 :

Is 2352 a perfect square? If not, find the smallest multiple of 2352 which is a perfect square. Find the square root of the new number

Solution

Problem 11 :

Find the least number which should be subtracted from 180 to make it a perfect square.

Solution

Problem 12 :

The length of a rectangle is 3 times its width. Its area is 972 sq. meter. Find the perimeter of the rectangle

Solution

Problem 13 :

A rectangle ABCD has AB = 12 cm and BC = 6 cm. Find the length of its diagonals correct to 2 decimal places.

Solution

Problem 14 :

Find the number of non-square numbers lying between 40² and 41².

a) 80     b) 40   c) 30     d) 84

Solution

Problem 15 :

If m, n, p are natural numbers such that (m, n, p) forms a Pythagorean triplet if ?

a) m² + n² = p²      b) m² + n² < p²    d) m² + n² ≠ p

Solution

Problem 16 :

The square of an even number is always____________.

a) even     b) odd     c)  may be even or odd      d)  none

Solution

Problem 18 :

The digit in the unit’s place in the square root of 15876 is

a) 8     b)  6       c)  4    d)  2

Solution