Question

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

Answer 1

Hint: Here we will use the concepts of the square and square root and will simplify the given expression and will use the property that square and square root cancel each other.

Complete step-by-step solution:
Take the given expression: $\sqrt {8{x^2}} $
The above equation can be re-written as using the product of the numbers.
$ \Rightarrow \sqrt {2 \times 4{x^2}} $
Square is the number multiplied with itself twice. Therefore, we can write $4 = {2^2}$
$ \Rightarrow \sqrt {2 \times {2^2} \times {x^2}} $
When there is a product of two squares of the number, we can write the whole square to both the terms all together.
$ \Rightarrow \sqrt {2 \times {{(2x)}^2}} $
The above expression can be re-written as
$ \Rightarrow \sqrt 2 \times \sqrt {{{(2x)}^2}} $
Square and square root cancel each other in the above expression.
$ \Rightarrow \sqrt 2 \times 2x$
Simplify the above expression.
$\Rightarrow 2x\sqrt 2 $
Hence the required simplified solution is $\sqrt {8{x^2}} = 2x\sqrt 2 $

Additional Information: Constants are the terms with fixed values such as the numbers it can be positive or negative whereas the variables are terms which do not have any fixed values and are denoted by small alphabets such as x, y, z, a, b, etc. 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 ${2^3} = 2 \times 2 \times 2 = 8$.

Note: Square is the number multiplied itself and 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 ${2^2} = 2 \times 2 = 4$ . Know the difference between the squares and square roots and apply the concepts accordingly. Square is the number multiplied twice and square-root is denoted by $\sqrt {{n^2}} = \sqrt {n \times n} $ For Example: $\sqrt {{2^2}} = \sqrt 4 = 2$.