# Thread: What is wrong with these operations? My calculator produces a different answer

1. ## What is wrong with these operations? My calculator produces a different answer

In this book I'm reading, there are three problems I'm having a hard time with.

1. $\sqrt{12}\times\sqrt{5}=\sqrt{60}=2\sqrt{15}$

When I enter $\sqrt{12}\times\sqrt{5}$ on my TI-84+ and hit Enter, I get 7.745966692 instead.

2. $3\sqrt{2}\times4\sqrt{8}=12\sqrt{16}=48$

When I enter $3\sqrt{2}\times4\sqrt{8}$ on my TI-84+ and hit Enter, I get 48, so that answer agrees with the book.

3. $2\sqrt{10}\times6\sqrt{5}=12\sqrt{50}=60\sqrt{2}$

When I enter $2\sqrt{10}\times6\sqrt{5}$ on my TI-84+ and hit Enter, I get 84.85281374 instead.

Can anybody explain why my answer is different and what the book's answer means?

Roger

2. Originally Posted by jairtime
In this book I'm reading, there are three problems I'm having a hard time with.

1. $\sqrt{12}\times\sqrt{5}=\sqrt{60}=2\sqrt{15}$

When I enter $\sqrt{12}\times\sqrt{5}$ on my TI-84+ and hit Enter, I get 7.745966692 instead.

2. $3\sqrt{2}\times4\sqrt{8}=12\sqrt{16}=48$

When I enter $3\sqrt{2}\times4\sqrt{8}$ on my TI-84+ and hit Enter, I get 48, so that answer agrees with the book.

3. $2\sqrt{10}\times6\sqrt{5}=12\sqrt{50}=60\sqrt{2}$

When I enter $2\sqrt{10}\times6\sqrt{5}$ on my TI-84+ and hit Enter, I get 84.85281374 instead.

Can anybody explain why my answer is different and what the book's answer means?

Roger
Hello,

your calculator is not able to handle symbols like $\sqrt{\ \ }$. It has a build-in function which returns an approximative value. For instance: If you type $\sqrt{15}$ the calculator uses 3.872983346.. and as far as I'm informed the TI84 uses internally(?) 14 decimals and rounds a result down to maximal 12 decimals.

So considering the abilities of your calculator all results are OK.

If you take #1:

1. $\sqrt{12}\times\sqrt{5}=\sqrt{60}=\sqrt{4 \cdot 15} = 2\sqrt{15}$

This method is called calculating a root partially: A value is transformed into a product of a square and a non-square(?). You can calculate the square-root of the square. But your calculator isn't able to do these transformations.

3. ## Thanks

Thanks again, Earboth.

It puts a smile on my face to know that it's the calculator. I'm glad you know the answers to my questions!

I wonder if my new TI-89 Titanium can handle the problem.

Talk with you soon!

Roger

4. The very inexpensive Casio fx 83ES will give answers in surd form.

Of course where you're asked to do this in a test you won't be allowed to use a calculator, I'm guessing.