Question

How do you simplify $\sqrt{350}$?

Answer 1

Hint: The square root $\sqrt{x}$ of a given variable x is equal to a value which when multiplied by itself will give x. It is like an inverse function of squaring. To simplify the given square root we have to find out its factors so that we can identify this pattern.

Complete Step by Step Solution:
The given square root value is $\sqrt{350}$.
Let us now factorize the number 350 to find out its factors.
$\Rightarrow \sqrt{350}=\sqrt{2\times 5\times 5\times 7}$
Here we can see that $5\times 5={{5}^{2}}$ and we know that the square is an inverse function of its square root. Therefore they will cancel each other ie., $\sqrt{{{5}^{2}}}=5$. So, we can take the factor 5 out of the square root.
$\Rightarrow \sqrt{350}=5\sqrt{2\times 7}$
$\Rightarrow \sqrt{350}=5\sqrt{35}$

Hence the simplified form of $\sqrt{350}$ is equal to $5\sqrt{35}$.

Note:
The cube of a given variable x is equal to x raised to the power of three (${{x}^{3}}$). The cube root is an inverse function of the cube. Therefore they will cancel each other ie.,$\sqrt[3]{{{x}^{3}}}=x$. Generally, the root function can have any degree and so we can state that $\sqrt[n]{{{x}^{n}}}=x$.