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Square Root Quiz

Note: Information to help answer these quiz questions can be found on the SquareRootCalculator.Co website.

1. How many square roots does a number have?    
   answer
   
   A number has two roots: a positive square root and a negative square root (with the exception of the number 0 which has only one square root...0).
   
   
2. If you have an equation like: N² = 15
   How do you solve for N?    
   answer
   
   Taking the square root of both sides of the equation yields:
   √ N²     =   √ 15  
   N = √ 15  
   N = 3.8729833
   
   
3. If you have an equation like: √ N   = 7
   How do you solve for N?    
   answer
   
   Squaring both sides of the equation yields:
   √ N   ²   =   7²
   N = 49
   
   Or, inputting the number 7 into the answer side of the square root calculator will give:
   square root of 49 = 7
   
   
   
4. The radical sign √    refers to the __________ of a number.    
   1. positive square root
   2. negative square root
   3. both the positive and negative square root
   answer
   
   a. positive square root
   
   
5. The square root of a negative number will be a/an __________ number.    
   1. negative
   2. imaginary
   3. real
   answer
   
   b. imaginary
   
   
6. Using the square root calculator, what is the square root of the complex number 6+5i ?    
   answer
   
   √ 6+5i   = 2.6277604+0.9513805i
   
   
7. If the area of a circle is 30 inches², what is the side length of a square with the same area?    
   answer
   
   Taking the square root of the area of any shape will yield the side length of a square with the same area.
   √ 30   = 5.4772256     Thus, a square with side length 5.4772256 inches has an area of 30 inches².
   
   
8. What scale factor would you use to double the area of an octagon?
   What scale factor would you use to triple the area of an octagon?    
   answer
   
   Scale factor and area are related by:
   new area = old area x (scale factor)²
   Thus, to double the area of any shape (octagon, square, circle, etc.), use a scale factor of √ 2  .
   To triple the area of any shape, use a scale factor of √ 3  .
   
   
9. What is the square root of 32 (to three decimal places) without using a calculator?    
   answer
   
   from Square roots without a calculator
   With an initial estimate (G1) of 6:
   G1 = 6
   G2 = (32/6 + 6) /2 = 5.6667
   G3 = (32/5.6667 + 5.6667) /2 = 5.6569
   G4 = (32/5.6569 + 5.6569) /2 = 5.6569
   
   Check progress:   5.6569 x 5.6569 = 32.0005
   Thus, the square root of 32 to three decimal places is 5.657
   
   

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