Question

How do you find the square root of 36/49?

Answer 1

`sqrt(36/49)=color(green)(6/7)`

Explanation:

In general
`color(white)("XXX")sqrt(a/b)=sqrt(a)/sqrt(b)`

`sqrt(36)=6`

`sqrt(49)=7`

So
`color(white)("XXX")sqrt(36/49)=sqrt(36)/sqrt(49)=6/7`

Answer 2

Answer is: `+- 6/7`, see explanation for steps.

Explanation:

Remember, or take a moment to learn, that:

`sqrt (x/y) = sqrtx / sqrty`

To find the square root of a fraction, we can simply find the square root of the numerator and denominator:

`sqrt36/sqrt49`

Either by using a calculator or recalling information, we come to find that:

`sqrt36 = +-6`

and

`sqrt49 = +-7`

The simplified answer can be retrieved from this. So, to write this as a fraction:

`+-6//+-7`

or

`+- 6/7`

**The `+-` indicates that a number can be positive or negative, and in this case we use this symbol since the square root of a positive number always has a positive and negative answer. For example, if you multiply `6` by itself, you get `36`. If you multiply `-6` by itself, you get `36` as well. This is why we include the `+-` symbol, and it is the correct form of writing your answers.