Question

How do you simplify $ \sqrt {132} $ ?

Answer 1

Hint: As we know that square root can be defined as a number which when multiplied by itself gives a number as the product. For example $ 5\times 5 = 25 $ , here square root of $ 25 $ is $ 5 $ . There is no such formula to calculate square root formula but two ways are generally considered. They are the prime factorization method and division method. The symbol $ \sqrt {} $ is used to denote square roots and this symbol of square roots is also known as radical.

Complete step-by-step answer:
Here we have $ \sqrt {132} $ which is a non perfect square i.e. an irrational number. So we have to factorise what is inside the square root.
 $ \sqrt {132} $ can be written as $ \sqrt {2\times2\times3\times11} $ , also
 $ \sqrt {4\times3\times11} = \sqrt 4 \times\sqrt {3\times11} $ .
Here 4 is a perfect square, so $ \sqrt {132} = 2\times\sqrt {33} $ .
As $ \sqrt {33} $ cannot be factored further or it can be converted into a decimal form.
Hence the simplified value of $ \sqrt {132} $ is $ 2\sqrt {33} $
So, the correct answer is “ $ 2\sqrt {33} $ ”.

Note: The above given numbers are non-perfect squares as we know that a non-perfect square is a number that there is no rational number i.e. it is considered as an irrational number. Their decimal does not end and they do not repeat a pattern so they are also non-terminating and non-repeating numbers. The number written inside the square root symbol or radical is known as radicand. We know that all real numbers have two square roots, one is a positive square root and another one is a negative square root. The positive square root is also referred to as the principal square root