# Mastering Square Roots: Simplifying Division, Addition, and Subtraction

• w3tw1lly

#### 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:

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

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

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

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.]

cristo said:
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 let's 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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"When you are simplifying roots, and you take out let's say the root of 4, do you times the number already outside the root sign by 2?"

Yes.

Also, remember to rationalize the fraction^^

w3tw1lly said:
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 let's 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?

w3tw1lly said:
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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## 1. What are square roots?

Square roots are a mathematical concept that involves finding a number that, when multiplied by itself, gives a specified number. For example, the square root of 25 is 5 because 5 x 5 = 25.

## 2. How do I simplify square roots?

To simplify a square root, you need to find the largest perfect square that is a factor of the number inside the radical symbol. Then, you can take the square root of that perfect square and move it outside of the radical symbol. Any remaining numbers inside the radical symbol can be left as is.

## 3. How do I divide square roots?

To divide square roots, you can simplify each individual square root using the method mentioned above. Then, you can divide the numbers outside the radical symbol and the numbers inside the radical symbol separately. Finally, simplify the resulting fraction if possible.

## 4. Can I add or subtract square roots?

Yes, you can add or subtract square roots as long as the numbers inside the radical symbol are the same. If they are not the same, you will need to simplify them first using the method mentioned above.

## 5. What are some tips for mastering square roots?

One tip for mastering square roots is to practice simplifying them regularly. Additionally, memorizing common perfect squares can make the simplification process quicker. Another helpful tip is to work backwards and check your answer by squaring it to see if it equals the original number.