# Square root questions

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:

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

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

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

## Answers and Replies

cristo
Staff Emeritus
Science Advisor
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.]

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.]
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)

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hage567
Homework Helper
"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.

Also, remember to rationalize the fraction^^

cristo
Staff Emeritus
Science Advisor
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)

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

Can you simplify this?

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:

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

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

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

can you go from here??

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 [Broken]

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