# What is Square root of 464 in simplest radical form?

May 20, 2017

$4 \sqrt{29}$

#### Explanation:

First, we look for any perfect squares that could be a factor of $\sqrt{464}$ by finding factors of 464 that divide in evenly.

$\frac{464}{4} = 116$
$\frac{464}{9} = 51.5555$
$\frac{464}{16} = 29$

It seems that 16 will be our highest factor, as it results in an answer of a prime #.

Now, we rework the equation as so:

$\sqrt{464}$ = $\sqrt{16 \cdot 29}$ = $\sqrt{16} \cdot \sqrt{29}$

Which simplifies into:

$\sqrt{16} \cdot \sqrt{29}$ = $4 \cdot \sqrt{29}$ = $4 \sqrt{29}$

Final answer: $4 \sqrt{29}$

May 20, 2017

$4 \sqrt{29}$

#### Explanation:

For questions dealing with factors, roots, HCF and LCM of numbers, a good starting point is to write the number(s) as the product of the prime factors:

$464 = 2 \times 2 \times 2 \times 2 \times 29$

Now we know what we are working with!

$\sqrt{464} = \sqrt{{2}^{4} \times 29} \text{ } \leftarrow$ (index of 2 is even, $\div 2$)

$= {2}^{2} \sqrt{29}$

$= 4 \sqrt{29}$

$29$ is a prime number, so we leave it as $\sqrt{29}$, nothing can be done there!