Question

How do you find the square root of \[\dfrac{3}{4}\] .?

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 we have a fraction. We solve this by finding the square root of the numerate and the square root of the denominator. Then dividing we get the required result.

Complete step-by-step answer:
Given, square root of \[\dfrac{3}{4}\] .
That is \[\sqrt {\dfrac{3}{4}} \] this can be written as \[\dfrac{{\sqrt 3 }}{{\sqrt 4 }}\] .
Now let’s find the square root of \[3\] . Since 3 is a small number the factors are only 1 and 3. We keep it as it is.
Now let’s find the square root 4. The factors of 4 are 2 and 2. That is 2 is multiplied twice. Hence the square root of 4 is 2. \[ \Rightarrow \sqrt 4 = 2\] .
Hence we have,
 \[\sqrt {\dfrac{3}{4}} = \dfrac{{\sqrt 3 }}{2}\] . This is the exact from.
We can write it in decimal form.
We know that \[\sqrt 3 = 1.732\] .
 \[ = \dfrac{{1.732}}{2}\]
 \[ = 0.866\] . This is in the decimal form.
So, the correct answer is “0.866”.

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. The set of prime numbers obtained that are multiplied to each other to form the bigger number are called the factors.