What is the square root of 90 simplified in radical form?

1 Answer
Jul 13, 2016

sqrt(90) = 3sqrt(10)

Explanation:

To simplify sqrt(90), the goal is to find numbers whose product gives the result of 90, as well as collect pairs of numbers to form our simplified radical form.

In our case, we can begin in the following way:

90 -> (30 * 3)

30 -> (10 * 3) ... *... 3

10 -> (5 * 2) ...... *... underbrace(3*3)_(pair)

Since we don't have numbers we could further divide which yield a number other than 1, we stop here and collect our numbers.

A pair of numbers counts as one number, namely the 3 itself.

Thus we can now write sqrt(90) = 3sqrt(5*2) = 3sqrt(10)

More examples:

(1) sqrt(30)

30 -> (10 * 3)
10 -> (5 * 2) ... * ... 3

We cannot find any more divisible factors, and we certainly don't have a pair of numbers, so we stop here and call it not simplify-able. The one and only answer is sqrt(30).

(2) sqrt(20)

20 -> (10 * 2)
10 -> (5) * underbrace(2 * 2)_(pair)

We've found a pair, so we can simplify this one:

sqrt(20) = 2sqrt(5)

(3) sqrt(56)

56 -> 8 * 7
8 -> 4 * 2 * 7
4 -> underbrace(2* 2)_(pair) * 2 * 7

We proceed the same way and write sqrt(56) = 2sqrt(2*7) = 2sqrt(14)