Please explain how to get the sqaure root of this number without a calculator? square root of 256

Question

Square root

Answer 1

You will find that in your mathematical studies, which will be part of every year of your high school and probably much of your college, that IT IS VERY IMPORTANT TO RECOGNIZE POWERS of small integers.

 

Start with memorizing the POWERS OF 2,namely 2,4,8, 16, 32, 64 (=2⁶), 128, 256, 512 1024, 4096 (=2¹²) and a few beyond.  Make flash cards, if needed.

 

Powers of 3: 3, 9, 27, 81, 243, 729.

 

Powers of 5: 5, 25, 125, 625, 3125.

 

Powers of 7: 7, 49, 343,2401.

 

If a number is not a perfect square, then its square root is IRRATIONAL;it's helpful to know that √2 is about 1.4142 and √3 is about 1.7321

 

No longer do schools teach how to do extraction of square roots by paper and pencil methods; any calculator can give you a good approximate decimal value.

 

The above suggested memorization-of-powers is a very serious recommendation; you will find that working with logarithms in Algebra II will be made much easier and understandable if you already carry the knowledge of those basic facts.

Answer 2

  

             √256

 

separate the numbers into groups of 2 starting on the right side

what is the largest number squared that goes into 2 ?

that number is 1

put 1 above the 2 and on the left of the radical

 

                 1

                 _______

       1      √2   56

 

1*1=1 so put 1 under the 2

 

 

                 1

                 ________

       1      √2   56

                 1

subtract and bring down 56 and double the 1 in the quotient

put 2 next to the 1 after subtracting

                  1

                  ________

        1      √2   56

                  1

                 _________

     

         2        1   56

choose the largest number, call it x, that can be put next to the 2 and above the 56 such that x*2x does not exceed 156

that number is 6 because 6*26=156

now you have the answer which is 16

 

another example:

 

 

                     √66564

   

                         2    5     8

                         __________

                2     √6   65   64

                         4

                       __________

                45      2   65

                          2   25

                       _________

                508          40  64

                                40  64

                               _______

                                        0

      

 this method is very time consuming, especially if the number is very large or if you want several digits in the answer of a number like √7

if you don't have a perfect square you can use trial and error

√7=?

the largest number squared less than 7 is 2

try 2.5 squared which is 6.25

try 2.6 squared which is 6.76

try 2.7 squared which is 7.29 which is too big

so we have 2.6 so far

try 2.65 squared which is 7.0225 which is too large

so we have to use 2.64

try 2.645 squared which is 6.996025

so far we have 2.645

try 2.6459 squared which is 7.0007868

try 2.6458 squared which is also to large

try 2.6457 squared which is 6.9997285

continue on until you have the correct number of digits that you want

by the way, √7=2.64575131...             

 

              

Answer 3

√256 = √(16²) = 16

Answer 4

Look at the unit digit in the number.  It is 6.  6 is not a perfect square, but the numbers 16 and 36 are.

 

4 x 4 = 16

 

6 x 6 = 36

 

 

We know that 14 x 14 is 196 using long multiplication.

 

Try 16 x 16 using long multiplication.

 

 

  16

x 16

____

  96

16

____

256

 

 

16² = 256