How to simplify tricky square roots with fractions?

[Isabel<3]

Hi, I'm in Algebra II and I have no idea how to solve these problems... I am not asking for the answer because the worksheet is just a completion grade, I am asking for help because we have to study that worksheet for a quiz tomorrow. We have notes but they don't clearly help with these problems and I cannot go in for tutoring because the quiz and the worksheet is due tomorrow, but her tutoring is after school only. Thanks in advance!

The worksheet says we have to simplify each expression and "rationalize denominators when necessary" (how do you know when to do that?) and then we have to round each simplified expression to the nearest whole number.

How do you solve a problems that look like these--> 4√8+3√72/-√50 and 7√3-12√3/√108

(√ = square root symbol; / = fraction bar)

 

[pka]

How do you solve a problems that look like these--> 4√8+3√72/-√50 and 7√3-12√3/√108

It is impossible to read what you posted.

For example: 4√8+3√72/-√50
Reads \(\displaystyle 4\sqrt8+\dfrac{3\sqrt{72}}{-\sqrt{50}}\).

Is that what you meant? I don't think so.

Use grouping symbols!

 

[Isabel<3]

It is impossible to read what you posted.

For example: 4√8+3√72/-√50
Reads \(\displaystyle 4\sqrt8+\dfrac{3\sqrt{72}}{-\sqrt{50}}\).

Is that what you meant? I don't think so.

Use grouping symbols!

I'm sorry, I tried to make it clear by putting this little "key": (√ = square root symbol; / = fraction bar)

I must admit that I am not very technology/computer savvy but now you're probably thinking that I am just not very savvy in the first place. Anyways, thank you very much for replying to this post, and you're right, that's not what I meant. I meant a fraction where (4√8+3√72) is the numerator and (-√50) is the denominator. Same goes for the other problem. Does that make (more) sense?

 

[pka]

I meant a fraction where (4√8+3√72) is the numerator and (-√50) is the denominator. Same goes for the other problem. Does that make (more) sense?

You can learn to use LaTeX.
[TEX]\dfrac{4\sqrt{8}+3\sqrt{72}}{-\sqrt{50}}[/TEX]

Gives \(\displaystyle \dfrac{4\sqrt{8}+3\sqrt{72}}{-\sqrt{50}}\)


[TEX]\sqrt{8}=\sqrt{4\cdot 2}=2\sqrt{2}[/TEX]
Gives \(\displaystyle \sqrt{8}=\sqrt{4\cdot 2}=2\sqrt{2}\)

[TEX]\sqrt{72}=\sqrt{9}\cdot\sqrt{8}=6\sqrt{2}[/TEX]
Gives \(\displaystyle \sqrt{72}=\sqrt{9}\cdot\sqrt{8}=6\sqrt{2}\)

[TEX]\sqrt{50}=5\sqrt{2}[/TEX]
Gives \(\displaystyle \sqrt{50}=5\sqrt{2}\)

 

[kanishkporwal]

When rationalizing denominator to simplify fractions we usually multiply and divide the fraction by conjugate.
It usually makes the fraction look better and hence is simplified easily.