Question

What is Square root of 464 in simplest radical form?

Answer 1

Hint: To obtain the simplest radical form of the square root of a given number we will use the factoring method. Firstly we will factorize the number given by using prime factorization then we will take out the factor with power in multiple of 2 as square mean a number multiplied by itself and square mean half of a square. Finally we will keep the terms that are not in multiple of 2 inside the square root sign and multiply the rest outside it to get the desired answer.

Complete step-by-step answer:
We have to find square root of following number in simplest radical form:
$464$
So we will start by finding prime factor of the number above as follows:
$\begin{align}
  & 2\left| \!{\underline {\,
  464 \,}} \right. \\
 & 2\left| \!{\underline {\,
  232 \,}} \right. \\
 & 2\left| \!{\underline {\,
  116 \,}} \right. \\
 & 2\left| \!{\underline {\,
  58 \,}} \right. \\
 & 29\left| \!{\underline {\,
  29 \,}} \right. \\
 & 1 \\
\end{align}$
We got the factor of 464 as below:
$464=2\times 2\times 2\times 2\times 29$
On simplifying we get:
$464={{2}^{4}}\times 29$
Next we have to find square root of above value so we get,
$\begin{align}
  & \sqrt{464}=\sqrt{{{2}^{4}}\times 29} \\
 & \Rightarrow \sqrt{464}={{2}^{4\times \dfrac{1}{2}}}\sqrt{29} \\
 & \Rightarrow \sqrt{464}={{2}^{2}}\sqrt{29} \\
 & \therefore \sqrt{464}=4\sqrt{29} \\
\end{align}$
We got the answer as $4\sqrt{29}$
Hence, Square root of 464 in simplest radical form is $4\sqrt{29}$

Note: When we have to find the square root of a number we are actually dividing the number in half. A number of the form $\sqrt{n}$ is a real number where $n$ is called the radicand and the symbol is known as radical symbol. We should know how to write the number given in radical form before solving it. The simplest form is the one where we take out the term outside the square root without any decimal values and rest values are kept inside the square root sign.