FINDING SQUARE ROOTS AND CUBE ROOTS WORKSHEET

Problem 1 : 

Solve for x :

x²  =  121

Problem 2 : 

Solve for x : 

x²  =  16/169

Problem 3 : 

Solve for x : 

x³  =  729

Problem 4 : 

Solve for x :

x³  =  8/125

Problem 5 : 

Find the square root of 0.16.

Problem 6 : 

Find the cube root of 0.008.

Problem 7 : 

Find the cube root of -125.

Problem 8 : 

Can you solve the equation x² = 27 and get a rational umber as solution ? Explain.  

Detailed Answer Key

Problem 1 : 

Solve for x :

x²  =  121

Solution :

x²  =  121

Solve for x by taking square root on both sides.

x  =  ± √121

Apply the definition of square root.

Think: What numbers squared equal 121 ?

x  =  ± 11

So, the solutions are 11 and −11.

Problem 2 : 

Solve for x : 

x²  =  16/169

Solution :

x²  =  16/169

Solve for x by taking square root on both sides.

x  =  ± √(16/169)

Apply the definition of square root.

Think: What numbers squared equal 16/169 ?

x  =  ± 4/13

So, the solutions are 4/13 and −4/13.

Problem 3 : 

Solve for x : 

x³  =  729

Solution :

x³  =  729

Solve for x by taking cube root on both sides.

x  =  ³√729

Apply the definition of cube root.

Think: What number cubed equals 729 ?

x  =  9

So, the solution is 9.

Problem 4 : 

Solve for x :

x³  =  8/125

Solution :

x³  =  8/125 

Solve for x by taking cube root on both sides.

x  =   ³√(8/125)

Apply the definition of cube root.

Think: What number cubed equals 8/125 ?

x  =  2/5

So, the solution is 2/5.

Problem 5 : 

Find the square root of 0.16.

Solution :

√0.16 = √(16/100)

=√16/√100

= 4/10

= 0.4

Problem 6 : 

Find the cube root of 0.008.

Solution :

³√0.008 = ³√(8/1000)

=³√8/³√1000

= 2/10

= 0.2

Solve for x by taking cube root on both sides.

x  =   ³√(8/125)

Apply the definition of cube root.

Think: What number cubed equals 8/125 ?

x  =  2/5

So, the solution is 2/5.

Problem 7 : 

Find the cube root of -125.

Solution :

³√-125 = ³√(-5 x -5 x -5)

= -5

Problem 8 : 

Can you solve the equation x² = 27 and get a rational umber as solution ? Explain.  

Solution :

No, we can not get a rational number as a solution. 

In the given equation we have "square" for "x".

So, we will be able to get a rational number as solution, only if we have a perfect square on the right side of the equation. 

Since we have 27 (not a perfect square) on the right side of the equation, we can not get a rational number as a solution. 

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