Question

What is square root 10 over square root 3 in simplest radical form

Answer 1

To simplify square root of 10 over square root of 3 in simplest radical form, multiply the numerator and denominator by the square root of 3 and then simplify.

Step-by-step explanation:

To simplify square root of 10 over square root of 3 in simplest radical form, we can rationalize the denominator. Rationalizing the denominator involves multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of the square root of 3 is also the square root of 3.

So, multiplying the numerator and denominator by the square root of 3, we get:

(square root of 10 * square root of 3) / (square root of 3 * square root of 3)

Simplifying further:

square root of 30 / 3

Therefore, square root of 10 over square root of 3 in simplest radical form is the square root of 30 divided by 3.

Answer 2

I'll give you a few examples of a square root over a square root first, so you'll understand how I got the answer:

1. √a / √b = √ab / b
2. √2 / √3 = √2*3 / 3 = √6 / 3
3. 1 / √a = √a / a
4. √3 / √7 = √21 / 7

I think you get how it works now.

Now lets solve the question.

√10 / √3
can also be written as √10 * 1/√3
1/√3 simplified is √3/3
So, √10 / √3 = √10 * √3/3
= √10*√3 / 3
= √30 / 3
Factor 30 (2*3*5) and make sure there are no pairs of factors that are the same. (for example: two 2's or two 4's)
If there are any pairs of factors, then take them outside the square root.
ex: √20 = √2*2*5 = 2√5

That was the long way to solve it, but there is a trick:
Remember what √a / √b equals?
It equals √a*b / b.
This means √10 / √3 is simply just √30 / 3.
Then all you need to do is make sure the number inside the radical has no pairs of factors then you are good to go.