Question

How do you simplify $\dfrac{{\sqrt 2 }}{{\sqrt 8 }}$?

Answer 1

Hint: Take the given expression and first find the equivalent term for the denominator finding the factors. Square is the number multiplied with itself and then simplified for the required value.

Complete step by step solution:
Take the given expression: $\dfrac{{\sqrt 2 }}{{\sqrt 8 }}$
The square root of a number is the number which is multiplied by the same number which gives the resultant original number. It is denoted by $\sqrt n $ where “n” can be any natural number.
Here, $\sqrt 8 = \sqrt {2 \times 2 \times 2} $
The above expression can be re-written as – $\sqrt 8 = \sqrt {2 \times 2 \times 2} = \sqrt {4 \times 2} = 2\sqrt 2 $
Place the above value in the given expression –
$\dfrac{{\sqrt 2 }}{{\sqrt 8 }} = \dfrac{{\sqrt 2 }}{{2\sqrt 2 }}$
Common multiple from the numerator and the denominator cancels each other. Therefore, remove
$\dfrac{{\sqrt 2 }}{{\sqrt 8 }} = \dfrac{1}{2}$
This is the required solution.

Thus the required solution is $\dfrac{{\sqrt 2 }}{{\sqrt 8 }} = \dfrac{1}{2}$.

Note: Know the concepts of squares and cubes. Square is the number multiplied itself and the cube it the number multiplied thrice. Square is the product of same number twice such as ${n^2} = n \times n$ for Example square of $2$ is ${2^2} = 2 \times 2$ simplified form of squared number is ${2^2} = 2 \times 2 = 4$. Cube is the product of same number three times such as ${n^3} = n \times n \times n$ for Example cube of $2$ is ${2^3} = 2 \times 2 \times 2$ simplified form of cubed number is ${2^3} = 2 \times 2 \times 2 = 8$.