PROBLEMS ON SQUARE ROOTS AND CUBE ROOTS WORKSHEET

Problem 1 :

If √1369 + √(0.0615) + x = 37.25, then x is equal to 

(a) 10^-1         (b) 10^-2           (c) 10^-3         (d) None

Solution

Problem 2 :

The sum of two numbers is 22 and the sum of their square is 404, then the product of the numbers is 

Solution

Problem 3 :

Solution

Problem 4 :

What is the value of in x in the following :

Solution

Problem 5 :

If 0.13 ÷ p² = 13, then p equals :

(a) 0.01    (b) 0.1    (c) 10    (d) 100

Solution

Problem 6 :

√3ⁿ = 729, then the value of n is

Solution

Problem 7 :

If √(18 ⋅ 14 ⋅ x) = 84, then x equals.

Solution

Problem 8 :

If 28√x + 1426 = 3/4 of 2872, then x equals.

Solution

Problem 9 :

If √x ÷ √441 = 0.02, then the value of x is :

Solution

Problem 10 :

If √(x - 1) (y + 2) = 7, x and y being whole numbers, then the values of x and y respectively are

(a)  8, 5   (b)  15, 12    (c)  22, 19    (d)  none

Solution

Problem 11 : 

If √(0.04 x 0.4 x a) = 0.004 x 0.4 x √b, then a/b is

Solution

Problem 12 :

Solution

Problem 13 :

If x = 7 - 4√3, then find the value of (x + 1/x) is

a)  3√3       b)  8√3     c)  14    d)  14 +  8√3

Solution

Problem 14 :

Th e ratio 125 : x is equivalent to the ratio x : 125. What is the value of x?

Solution

Problem 1 :

Find the value of following cube roots:

x = ∛(27 × 2744)

Solution

Problem 2 :

Evaluate 

Solution

Problem 3 :

Two numbers 4x and 5x are such that sum of their cubes is 189. Find x.

Solution

Problem 4 :

The volume of a cube is 5832 m³, find the length of the side.

Solution

Problem 5 :

Three numbers are in the ratio  3 : 4 : 5. If the sum of their cubes -1728, find the three numbers.

Solution

Problem 6 :

Check whether 648 is a perfect cube or not.

Solution

Problem 7 :

Three numbers are to one another as 2:3:4. The sum of their cubes is 33957. Find the numbers.

Solution

Problem 8 :

Solution

Problem 9 :

If y = 5, then what is the value of 10y√(y³ - y²) ?

Solution

Problem 10 :

Solution

Problem 11 :

Divide the number 26244 by the smallest number so that the quotient is a perfect cube, so he smallest number is :

a) 4     b) 6      c) 36      d) 16

Solution

Problem 12 :

The perfect cube nearest to 2750 is :

a) 2749     b) 2747      c) 2744      d) 2754

Solution

Problem 13 :

Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 98784. Find the numbers.

Solution

Problem 14 :

Three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 33957. Find the numbers.

Solution

Problem 15 :

Find the smallest number to be multiplied with 3600 will make the product perfect cube. Further find the cube root of the product.

Solution

Problem 1 :

The cube root of 125 × 64 is

a.   30     b. 20     c. 40     d. 10

Solution

Problem 2 :

Volume of cube is 343 cm³, its side is

a.   9 cm     b. 6 cm     c. 9 cm     d. 7 cm

Solution

Problem 3 :

The unit digit of cube of 7812 is

a.   8     b. 4     c. 2     d. 6

Solution

Problem 4 :

The cube root of 729 is

a.   3     b. 7     c. 9     d. 4

Solution

Problem 5 :

∛ 36 × 6 is

a.    6     b. 4     c. 16     d. 2

Solution

Problem 6 :

The cube of -1/2 is

a.    1/4     b. 1/8     c. -1/8     d. -8

Solution

Problem 7 :

By what number should 81 be multiplied to make it a perfect cube

a.   9     b. 1     c. 3     d. -3

Solution

Problem 8 :

Volume of cube whose edge is 4 cm

a.   64 cm³     b. 27 cm³     c. 2 cm³     d. 64cm²

Solution

Problem 9 :

Cube root of 0.001 is

a.   -0.1     b. -0.01     c. 0.1     d. -0.13

Solution

Problem 10 :

Cube root of (-7)³ × (-3)³ is

a.   -21     b. 21     c. -11     d. 10

Solution

Problem 11 :

Cube of -4/7 is

a.   -64/69    b. -64/49     c. -64/343     d. 64/343

Solution

Problem 12 :

Cube root of 0.001728 is

a.   0.12    b. -0.12     c. -10     d. -0.0012

Solution

Problem 13 :

Three numbers are in the ratio 3: 4: 5. If the sum of their cubes is -1728, find the three numbers.

Solution

Problem 14 :

Evaluate ∛5 1182/2197

Solution

Problem 15 :

Evaluate ∛ (-91125 × 512)

Solution

Problem 16 :

Shown is a cube with a volume of 8000 cm³

Solution

Problem 17 :

The number of two cubes are in the ratio of 343 : 1331, the ratio of their edges is :

a) 7: 10      b) 7 : 11     c) 7 : 12      d) 7 : 14

Solution

Problem 18 :

A 8 x 6 x 4 cm² metallic cube is melted. Find the minimum volume of the molten metal which should be added to mould it into a cube whose edge is an x , when x is an integer

Solution

Problem 19 :

√(5 + ∛x) = 3

a) ∛64     b)  64     c)  √4096     d) ∛262144

Solution