Question

How do you simplify \[\sqrt {0.5} \] ?

Answer 1

Hint: Square root of a number is a value, which on multiplied by itself gives the original number. Suppose, ‘x’ is the square root of ‘y’, then it is represented as \[x = \sqrt y \] or we can express the same equation as \[{x^2} = y\] . Here we can see that 0.5 is not a perfect square. Here we have a decimal point.

Complete step-by-step answer:
Given,
 \[\sqrt {0.5} \]
We know that 0.5 can be written in fraction. That is multiply and divide by 10.
We get, \[0.5 = \dfrac{{0.5 \times 10}}{{10}}\]
 \[ = \dfrac{5}{{10}}\]
 \[ \Rightarrow 0.5 = \dfrac{1}{2}\] .
Thus we have
 \[ \Rightarrow \sqrt {0.5} = \sqrt {\dfrac{1}{2}} \]
 \[ = \dfrac{1}{{\sqrt 2 }}\] . This is the exact form. We can stop here.
We also put it in the decimal form.
We know that \[\sqrt 2 = 1.414\] and multiplying this with 7 we get,
 \[ = \dfrac{1}{{1.414}}\]
 \[ = 0.70721\] . This is the decimal form.
So, the correct answer is “0.70721”.

Note: Here \[\sqrt {} \] is the radical symbol used to represent the root of numbers. The number under the radical symbol is called radicand. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number. To find the factors find the smallest prime number that divides the given number and divide it by that number, and then again find the smallest prime number that divides the number obtained and so on. The set of prime numbers obtained that are multiplied to each other to form the bigger number are called the factors.