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

• Dec 11th 2007, 06:13 PM
jairtime
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. $\displaystyle \sqrt{12}\times\sqrt{5}=\sqrt{60}=2\sqrt{15}$

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

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

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

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

When I enter $\displaystyle 2\sqrt{10}\times6\sqrt{5}$ 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
• Dec 11th 2007, 08:33 PM
earboth
Quote:

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

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

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

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

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

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

When I enter $\displaystyle 2\sqrt{10}\times6\sqrt{5}$ 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 $\displaystyle \sqrt{\ \ }$. It has a build-in function which returns an approximative value. For instance: If you type $\displaystyle \sqrt{15}$ 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. $\displaystyle \sqrt{12}\times\sqrt{5}=\sqrt{60}=\sqrt{4 \cdot 15} = 2\sqrt{15}$

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.
• Dec 11th 2007, 09:48 PM
jairtime
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
• Jan 14th 2008, 04:47 AM
a tutor
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. :)