What is the exact value of the expression 7the square root of 8. + 2the square root of 12. − 3the square root of 2.? Show your work. You can show a square root by writing "sqrt()". For example, the square root of 2 can be written as "sqrt(2)".

Question

anonymous · Answer

@surjithayer Help?

anonymous · Answer

Is this what you mean?
$$7\sqrt{8}+2\sqrt{12}-3\sqrt{2}$$

anonymous · Answer

Just saying "7 the square root of 8" are you implying "7 and the square root of 8?" which is the same thing "7 times the square root of 8?"

anonymous · Answer

Yes thats what I mean (:

anonymous · Answer

They don't want you to simplify? Unless you are an advanced calculus class, you will need a calculator.

The simplified form of this is

$$11\sqrt{2}+4\sqrt{3}$$

anonymous · Answer

Will you show your steps?

anonymous · Answer

Do you know how to simplify radicals at all?

anonymous · Answer

Do you know what a perfect square is?

anonymous · Answer

A perfect square is a number that has rational roots, basically they don't have decimal places that go on forever. Like 4 is a perfect square, because the square root of 4 is 2, which is rational. The square root of 5 however is some very long irrational number. So, a perfect square will come out "nicely" so to speak

anonymous · Answer

To simplify a radical, you look to see if that number is divisible by a perfect square. If it is, you look for the highest perfect square. Then, you take whatever number is multiplies by that perfect square to equal the original number under the radical.

EXAMPLE:
$$\sqrt{8}$$ Some small perfect squares: 4, 9, 16 - Ok, we're already clearly over this number, so the only perfect square that can go into 8 is 4. So, what times 4 is equal to 8? 2. so,
$$\sqrt{4\times2}$$

Now, 4 is a perfect square, so you can go ahead and do the square root of 4, which is 2.
So,
$$7\times2\sqrt{2}$$ 4 came out of the radical, by taking the square root of 4, which is 2. The 2 is not a perfecet square, so it stayed under the radical. Don't forget the 7 that was there to begin with. So,

$$14\sqrt{2}$$

anonymous · Answer

So basically,
$$7\sqrt{8} simplifies \to 14\sqrt{2}$$
$$2\sqrt{12} simplifies \to 4\sqrt{3}$$
$$3\sqrt{2} doesn't simplify$$
You are left with
$$14\sqrt{2}+4\sqrt{3}-3\sqrt{2}$$
You have 2 square roots of 2, so just subtract 3 from 14
$$11\sqrt{2}+4$$

anonymous · Answer

Sorry, that's
$$4\sqrt{3}$$ computer keeps cutting it off.

anonymous · Answer

Ok thank you!

anonymous · Answer

Wait so its 11sqrt(2) + 4sqrt(3)?

anonymous · Answer

Correct. Remember that irrational numbers never end. So, this is the exact value. If you were to write it as a decimal, you would be approximating to a certain decimal place. As a decimal, it would never end.