Simplifying Surds

[BobbyPeterson32]

Hello,

I've got a question that I'm stuck on how to work out.

The question states Simplify the Surd [MATH]\frac{\sqrt[7]{5}}{\sqrt{35}}+\sqrt{63}[/MATH] and to answer it by writing it as a surd in it's simplest form.

In my head, I simplify the roots which I think? only [MATH]\sqrt{63}[/MATH] can be simplified via [MATH]\sqrt{9}\:\cdot \:\sqrt{7}\:=\:\sqrt[3]{7}[/MATH]
and that's as far as I can get, I've looked at my workbooks, youtube etc... and I just can't get my head around what to do with the first part because the examples I found online say to divide the root numbers so in this case 3 and 2 and then the whole numbers so 5 and 35 but these leave me with decimal numbers that I can't find nth numbers to go into; 2⁷ is already 128 and using above I've got 3.5 and 0.142... it's baffles me.

Any help and explanations would be appreciated. I've spent hours on it so far and I'm getting nowhere.

 

[pka]

The question states Simplify the Surd [MATH]\frac{\sqrt[7]{5}}{\sqrt{35}}+\sqrt{63}[/MATH] and to answer it by writing it as a surd in it's simplest form.
In my head, I simplify the roots which I think? only [MATH]\sqrt{63}[/MATH] can be simplified via [MATH]\sqrt{9}\:\cdot \:\sqrt{7}\:=\:\sqrt[3]{7}[/MATH]

There is a mistake in the above: \(\sqrt{9}\:\cdot \:\sqrt{7}\:\ne\:\sqrt[3]{7}\) But rather \(\sqrt{9}\:\cdot \:\sqrt{7}\:=3\sqrt{7}\)
Now simplifications are in the eye of the beholder. In addition to the correction I would do this:
\(\dfrac{\sqrt[7]{5}}{\sqrt{35}}\cdot\dfrac{\sqrt{35}}{\sqrt{35}}=?\) From which there are several ways to go.

 

[Dr.Peterson]

Hello,

I've got a question that I'm stuck on how to work out.

The question states Simplify the Surd [MATH]\frac{\sqrt[7]{5}}{\sqrt{35}}+\sqrt{63}[/MATH] and to answer it by writing it as a surd in it's simplest form.

In my head, I simplify the roots which I think? only [MATH]\sqrt{63}[/MATH] can be simplified via [MATH]\sqrt{9}\:\cdot \:\sqrt{7}\:=\:\sqrt[3]{7}[/MATH]
and that's as far as I can get, I've looked at my workbooks, youtube etc... and I just can't get my head around what to do with the first part because the examples I found online say to divide the root numbers so in this case 3 and 2 and then the whole numbers so 5 and 35 but these leave me with decimal numbers that I can't find nth numbers to go into; 2⁷ is already 128 and using above I've got 3.5 and 0.142... it's baffles me.

Any help and explanations would be appreciated. I've spent hours on it so far and I'm getting nowhere.

Since you wrote [MATH]\sqrt[3]{7}[/MATH] where you clearly meant [MATH]3\sqrt{7}[/MATH], I suspect the problem itself is written incorrectly with a seventh root, and should be this:

Simplify the Surd [MATH]\frac{7\sqrt{5}}{\sqrt{35}}+\sqrt{63}[/MATH]​

Please confirm that. Then I suggest rationalizing the denominator.