Question

How will you find the square root of \[320\]?

Answer 1

Hint:
In this question, we will first find the factors of \[320\] in exponential form. We will find the square root of the factors and find the solution for the square root of\[320\]. While finding the factors make sure that one of the factors is a square of any number. Sign convention should use properly while factorization.

Complete step by step solution:
Factors of \[320\] in exponential form can be given as,
\[320 = 64 \times 5 = 8 \times 8 \times 5\]
Now we will take square root of the above equation, we get,
\[\sqrt {320} = \sqrt {64 \times 5} \]
We know that, \[\sqrt {64} = 8\] , Putting this value in above equation, we get,
\[\therefore \sqrt {320} = 8\sqrt 5 \]
The value for \[\sqrt 5 \] is\[2.23606798\], putting this value in above equation, we get,
\[
  \sqrt {320} = 8 \times 2.23606798 \\
  \,\,\,\,\,\,\,\,\,\,\,\,\, = 17.885438 \\
 \]

Therefore, the square root of \[320\] is \[17.885438\].

Additional information:
The \[\sqrt {} \] symbol is called the radical sign. To simplify the square root of \[320\]means to find the simplest radical form of √320. The square root of \[320\] is an irrational number that is in decimal form. In order to find it one must know the \[\sqrt 5 \] value. Square roots are having a large application in mathematics. One should know the squares and square roots of basic numbers while solving mathematics problems.

Note:
Students should do the proper factorization of the number given .Students should know the square root of basic small numbers. Students should use proper sign convention while finding the factors. Students should be careful while forming factors. Multiplication should be done precisely. Writing 4 numbers after the decimal point is enough. Students are not supposed to write all the numbers after the decimal point.