Question

What is 3 divided by square root 3?

Answer 1

Hint: In this question, provided with two numbers. And we have to calculate the exact value by dividing one number with the other. Take the number with whom we are dividing the other number. Let choose the number 3 as dividend and take it as numerator and \[\sqrt 3 \] as divisor and take it as denominator and further simplify by using division operation to get the required value.

Complete step-by-step answer:
The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing. The division is an operation inverse of multiplication.
Consider, the given question
We have to find the exact value when 3 is divided by square root 3.
Here we consider 3 as dividend and take it as in the numerator and
Square root of 3 i.e., \[\sqrt 3 \] as a divisor takes it as in the denominator.
We can represent the given question in division form as:
 \[ \Rightarrow \dfrac{3}{{\sqrt 3 }}\]
Here, the denominator has radicand \[\sqrt 3 \] . To divide this we have to write a numerator in the form of radicand.
So numerator 3 can be written as \[3 = {\left( {\sqrt 3 } \right)^2}\] , on substituting we have
 \[ \Rightarrow \dfrac{{{{\left( {\sqrt 3 } \right)}^2}}}{{\sqrt 3 }}\]
 \[ \Rightarrow \dfrac{{\sqrt 3 \times \sqrt 3 }}{{\sqrt 3 }}\]
On cancelling the like terms in both numerator and denominator, we get
 \[ \Rightarrow \sqrt 3 \]
This cannot be simplified further without using a calculator, when using a calculator we get the exact value i.e.,
  \[ \Rightarrow \sqrt 3 \simeq 1.732050807569\]
Hence, it’s a required answer.
So, the correct answer is “$\sqrt 3$”.

Note: In this question, \[3\] is the dividend \[\sqrt 3 \] is the divisor and dividing these we got $\sqrt 3 $ as quotient and \[0\] is our remainder. We can also check our answer by using the dividend divisor remainder method. Where we can use the formula known as the remainder formula:
Dividend \[ \div \] divisor \[ = \] quotient \[ + \] remainder \[ \div \] divisor
Or can be written as
Dividend \[ = \] Quotient \[ \times \] divisor \[ + \] remainder.
 \[3 = \sqrt 3 \times \sqrt 3 + 0\]
 \[3 = {\left( {\sqrt 3 } \right)^2}\]
On simplification, we get
 \[3 = 3\]
Which verified our answer.