What is Square root of 464 in simplest radical form?

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What is Square root of 464 in simplest radical form?

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Answer 1 · 2017-05-20T06:17:25

$4 \sqrt{29}$ $4sqrt(29)$

Explanation:

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

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

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:

$\sqrt{464}$ $sqrt(464)$ = $\sqrt{16 \cdot 29}$ $sqrt(16*29)$ = $\sqrt{16} \cdot \sqrt{29}$ $sqrt(16)*sqrt(29)$

Which simplifies into:

$\sqrt{16} \cdot \sqrt{29}$ $sqrt(16)*sqrt(29)$ = $4 \cdot \sqrt{29}$ $4*sqrt(29)$ = $4 \sqrt{29}$ $4sqrt(29)$

Final answer: $4 \sqrt{29}$ $4sqrt(29)$

Answer 2 · 2017-05-20T08:36:53

$4 \sqrt{29}$ $4sqrt29$

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:

$464 = 2 \times 2 \times 2 \times 2 \times 29$ $464 = 2xx2xx2xx2 xx29$

Now we know what we are working with!

$\sqrt{464} = \sqrt{2^{4} \times 29} \leftarrow$ $sqrt464 = sqrt(2^4 xx29)" "larr$ (index of 2 is even, $\div 2$ $div2$ )

$= 2^{2} \sqrt{29}$ $= 2^2sqrt29$

$= 4 \sqrt{29}$ $=4sqrt29$

$29$ $29$ is a prime number, so we leave it as $\sqrt{29}$ $sqrt29$ , nothing can be done there!

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What is Square root of 464 in simplest radical form?

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