Question

What is Square root of 464 in simplest radical form?

Answer 1

`4sqrt(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.

`464/4 = 116`
`464/9 = 51.5555`
`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*29)` = `sqrt(16)*sqrt(29)`

Which simplifies into:

`sqrt(16)*sqrt(29)` = `4*sqrt(29)` = `4sqrt(29)`

Final answer: `4sqrt(29)`

Answer 2

`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 = 2xx2xx2xx2 xx29`

Now we know what we are working with!

`sqrt464 = sqrt(2^4 xx29)" "larr` (index of 2 is even, `div2`)

`= 2^2sqrt29`

`=4sqrt29`

`29` is a prime number, so we leave it as `sqrt29`, nothing can be done there!