Question

How do you simplify $\dfrac{2}{{\sqrt {10} }}$?

Answer 1

Hint: To solve such questions first multiply the numerator and denominator by $\sqrt {10}$. Next, simplify the denominator. Finally cut out the common factor in the numerator and denominator. An algebraic expression can also be simplified by taking together all the like terms.

Complete step-by-step answer:
Given the equation $\dfrac{2}{{\sqrt {10} }}$.
Here it is asked to simplify the given equation.
First, start by multiplying both the numerator and denominator of $\dfrac{2}{{\sqrt {10} }}$ with $\sqrt {10}$.
That is,
$\dfrac{2}{{\sqrt {10} }} \times \dfrac{{\sqrt {10} }}{{\sqrt {10} }}$
Next, simplify the above equation. That is,
$\dfrac{2}{{\sqrt {10} }} \times \dfrac{{\sqrt {10} }}{{\sqrt {10} }} = \dfrac{{2\sqrt {10} }}{{10}}$
Finally, cancel out the common numbers in the numerator and denominator. That is,
$\dfrac{{2\sqrt {10} }}{{10}} = \dfrac{{\sqrt {10} }}{5}$

Therefore, the simplified form of $\dfrac{2}{{\sqrt {10} }}$is $\dfrac{{\sqrt {10} }}{5}$.

Additional information:
Variables can be defined as a quantity that is not fixed. An algebraic expression can be made up of variables, constants, and operators. An equation can be defined as one which allows only a specific value of a variable. For a given term to be an equation, the left-hand side should be equal to the right-hand side. If they are not equal then it cannot be an equation. The value of the variable, which we get by solving the equation, is known as the solution of the equation.

Note:
Always remember that when we have to write an equation that is in the form $\dfrac{a}{{\sqrt b }}$ to the form $\dfrac{{c\sqrt d }}{e}$ then we have to multiply both the numerator and denominator of $\dfrac{a}{{\sqrt b }}$ by $\sqrt b$. After multiplication, if there are any common factors for the numerator and denominator then cancel them. Whenever there is an irrational number in the denominator, always remember to make it rational by multiplying and dividing the given equation with the irrational number.