Square root questions

1. Apr 4, 2007

w3tw1lly

I feel embarassed to ask these questions but what is the rule for to simplify division, addition, and subtraction square roots? Here are some questions:

SIMPLIFY:

$$5\sqrt{24}\div2\sqrt{18}$$

$$\sqrt{40} + \sqrt{90}$$

$$\sqrt{50} - \sqrt{18}$$

2. Apr 4, 2007

cristo

Staff Emeritus
What have you tried? You need to simplify the square roots. For example, write the first question as $$\frac{5\sqrt{24}}{2\sqrt{18}}$$ Now, can you simplify $\sqrt{24}$ and $\sqrt{18}$?

[Hint: write each number under the sqrt sign as a product of primes.]

3. Apr 4, 2007

w3tw1lly

Sorry, I meant to write the question like a fraction I just didn't know the code. When you are simplifying roots, and you take out lets say the root of 4, do you times the number already outside the root sign by 2?

$$\frac{5\sqrt{24}}{2\sqrt{18}}$$
=$$\frac{5\sqrt{4*6}}{2\sqrt{3*6}}$$ (don't know what to do, so long since we had done radicals)

Last edited: Apr 4, 2007
4. Apr 4, 2007

hage567

"When you are simplifying roots, and you take out lets say the root of 4, do you times the number already outside the root sign by 2?"

Yes.

5. Apr 4, 2007

Feldoh

Also, remember to rationalize the fraction^^

6. Apr 5, 2007

cristo

Staff Emeritus
$$\frac{5\sqrt{4*6}}{2\sqrt{3*6}}=\frac{5\cdot 2\cdot\sqrt{6}}{2\cdot\sqrt{3}\cdot\sqrt{6}}$$

Can you simplify this?

7. Apr 5, 2007

sutupidmath

$$\sqrt{40} + \sqrt{90}$$=$$\sqrt{4*10}+\sqrt{9*10}$$=2$$\sqrt{10}+3\sqrt{10}$$=

can you go from here??

8. Apr 5, 2007

thomas49th

this may confuse you more but when you add fractions you need to get the denominator (number on the bottom of fraction) the same. The same goes with surds (square roots), you need to get the number inside the root the same on each surd in oder to add/subtract.

I find it harder to do the + - surds than the x and / surds

When you divide:
$$\sqrt{a} \div \sqrt{b} = \frac {\sqrt{a}}{\sqrt{b}}$$ which is also written as $$\sqrt{\frac{a}{b}}$$

Have a look

http://www.mathsrevision.net/gcse/pages.php?page=6

and

http://www.bbc.co.uk/schools/gcsebitesize/maths/numberih/surdshrev2.shtml

Last edited by a moderator: Apr 22, 2017