GCSE Mathematics Number deaf

Add and subtract deaf

Here we will meet you**Add and subtract deaf**including when unvoiced expressions can be added or subtracted and how these calculations are performed.

There are also worksheets for adding and subtracting surds based on Edexcel, AQA, and OCR exam questions, along with more guidance on what to do next if you're still stuck.

## What is deaf add and subtract?

When adding and subtracting surdos, we can add or subtract surdos when the numbers under the root symbols (the radicands) are equal; these are called "like deafs".

This is similar to collecting like terms in algebra:

Z.B.

So if we do something similar with surds:

Z.B.

\[\sqrt{3}+\sqrt{3}+2\sqrt{3}=4\sqrt{3}\]

It's the same

2\sqrt{3}+3\sqrt{7}it cannot be simplified because the numbers under the square root (radical) symbols are different.\sqrt{3}E\sqrt{7}they are not "like deaf people".

If surds can be simplified to be "like surds", then they can be added or subtracted.

You may be asked to apply these skills to GCSE math to give answers to geometry problems such as Pythagoras or trigonometry in exact values rather than decimals. Before calculators were invented, surds were the standard way to give answers, which were irrational numbers.

The formula for solving the quadratic also uses a square root sign, so you may need to apply your knowledge of surds here as well.

### What is deaf add and subtract?

## How to add and subtract deaf

To add and subtract voiceless:

**Make sure the terms are "like surds".****If they are not like surds, simplify each surd as much as possible.****Combine like unvoiced terms by adding or subtracting.**

### How to add and subtract deaf

### Worksheet for adding and subtracting deaf

Get your free addition and subtraction worksheet with 20+ questions and answers. Contains justifications and applied questions.

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### Worksheet for adding and subtracting deaf

Get your free addition and subtraction worksheet with 20+ questions and answers. Contains justifications and applied questions.

DOWNLOAD FOR FREE

## Examples of deaf addition and subtraction

### Example 1: like surds, simple addition

Simplify

\[2\sqrt{3}+5\sqrt{3}\]

**Make sure the terms are "like surds".**

The number under the root sign is already

**2If they are not like surds, simplify each surd as much as possible.**

We don't need to change the deaf terms in this question.

**3Combine like unvoiced terms by adding or subtracting.**

\[2+5=7\]

Then,

\[2\sqrt{3}+5\sqrt{3}=7\sqrt{3}\]

### Example 2: like surds, simple subtractions

Simplify

\[7\sqrt{5}-9\sqrt{5}+6\sqrt{5}\]

**Make sure the terms are "like surds".**

The number under the root sign is already

**If they are not like surds, simplify each surd as much as possible.**

We don't need to change the deaf terms in this question.

**Combine like unvoiced terms by adding or subtracting.**

\[7-9+6=4\]

Then,

\[7\sqrt{5}-9\sqrt{5}+6\sqrt{5}=4\sqrt{5}\]

### Example 3: As opposed to surds

Simplify

\[10 \sqrt{2}+4 \sqrt{11}\]

**Make sure the terms are "like surds".**

The numbers under the root signs are

**If they are not like surds, simplify each surd as much as possible.**

These deaf ones cannot be simplified any further. There are no square factors for any of them.

**Combine like unvoiced terms by adding or subtracting.**

In this case, the deaf are not the same, so they cannot be combined.

In response we give:

\[10 \sqrt{2}+4 \sqrt{11}\]

### Example 4: Totals Containing Unvoiced

Simplify

\[4+6\sqrt{2}-3\sqrt{2}-\sqrt{25}\]

**Make sure the terms are "like surds".**

All surd terms are like surds - all are root

**If they are not like surds, simplify each surd as much as possible.**

We don't need to simplify the deaf.

However, the square root of

\[4+6\sqrt{2}-3\sqrt{2}-5\]

**Combine like unvoiced terms by adding or subtracting.**

Combining the deaf:

\[6\sqrt{2}-3\sqrt{2}=3\sqrt{2}\]

We also combine the other like terms - in this case the integers:

\[ 4-5=-1\]

So the final answer is:

\[3\sqrt{2}-1\]

Note that it's always best to start an answer with a positive term, but:

\[-1+3\sqrt{2}\]

is also correct.

### Example 5: A deaf person needs to be simplified

Simplify

\[\sqrt{7}+\sqrt{28}\]

**Make sure the terms are "like surds".**

The numbers under the root signs are

**If they are not like surds, simplify each surd as much as possible.**

\[\sqrt{7}\]

it is already fully simplified; there are no square factors of

\[\sqrt{28}\]

can be simplified because

\[\begin{aligned}\sqrt{28} &=\sqrt{4 \times 7} \\&=\sqrt{4} \times \sqrt{7} \\&=2 \times \sqrt{7} \\&=2 \sqrt{7}\end{alinhado}\]

**Combine like unvoiced terms by adding or subtracting.**

\[\begin{aligned}\sqrt{7}+\sqrt{28} &=\sqrt{7}+2 \sqrt{7} \\&=3 \sqrt{7}\end{aligned}\]

### Example 6: Both deaf need to be simplified

Simplify

\[\sqrt{8}+\sqrt{72}\]

**Make sure the terms are "like surds".**

The numbers under the root signs are

**If they are not like surds, simplify each surd as much as possible.**

\[\sqrt{8}\]

can be simplified because

\[\begin{aligned}\sqrt{8} &=\sqrt{4 \times 2} \\&=\sqrt{4} \times \sqrt{2} \\&=2 \times \sqrt{2} \\&=2 \sqrt{2}\end{alinhado}\]

\[\sqrt{72}\]

can be simplified because

\[\begin{aligned}\sqrt{72} &=\sqrt{36 \times 2} \\&=\sqrt{36} \times \sqrt{2} \\&=6 \times \sqrt{2} \\&=6 \sqrt{2}\end{alinhado}\]

Note that you can simplify incrementally using the squared factors

\[\begin{aligned}\sqrt{72} &=\sqrt{4} \times \sqrt{18} \\&=2 \sqrt{18}\end{aligned}\]

So the deaf ones wouldn't be "like" and you couldn't combine by addition or subtraction.

**Combine like unvoiced terms by adding or subtracting.**

\[\begin{aligned}\sqrt{8}+\sqrt{72} &=2\sqrt{2}+6 \sqrt{2} \\&=8 \sqrt{2}\end{aligned}\]

### Example 7: Two deaf people need to be simplified

Simplify

\[\sqrt{75}+\sqrt{50}\]

**Make sure the terms are "like surds".**

The numbers under the root signs are

**If they are not like surds, simplify each surd as much as possible.**

\[\sqrt{75}\]

can be simplified because

\[\begin{aligned}\sqrt{75} &=\sqrt{25 \times 3} \\&=\sqrt{25} \times \sqrt{3} \\&=5 \times \sqrt{3} \\&=5 \sqrt{3}\end{alinhado}\]

\[\sqrt{50}\]

can be simplified because

\[\begin{aligned}\sqrt{50} &=\sqrt{25 \times 2} \\&=\sqrt{25} \times \sqrt{2} \\&=5 \times \sqrt{2} \\&=5 \sqrt{2}\end{alinhado}\]

**Combine like unvoiced terms by adding or subtracting.**

Even when fully simplified, the deaf are not similar, so they cannot be combined.

In response we give:

\[5\sqrt{3}+5\sqrt{2}\]

### Example 8: a total containing non-deaf people

Simplify

\[\sqrt{90}+\sqrt{64}-\sqrt{40}\]

**Make sure the terms are "like surds".**

The numbers under the root signs are

**If they are not like surds, simplify each surd as much as possible.**

\[\sqrt{90}\]

can be simplified because

\[\begin{aligned}\sqrt{90} &=\sqrt{9 \times 10} \\&=\sqrt{9} \times \sqrt{10} \\&=3 \times \sqrt{10} \\&=3 \sqrt{10}\end{alinhado}\]

\[\sqrt{64}=8\]

\[\begin{aligned}\sqrt{40} &=\sqrt{4 \times 10} \\&=\sqrt{4} \times \sqrt{10} \\&=2 \times \sqrt{10} \\&=2 \sqrt{10}\end{alinhado}\]

**Combine like unvoiced terms by adding or subtracting.**

\[\begin{aligned}\sqrt{90}+\sqrt{64}-\sqrt{40} &=3 \sqrt{10}+8-2 \sqrt{10} \\&=8+\sqrt{ 10}\end{alinhado}\]

### common misunderstandings

**Remember that a square root with no integer coefficient "1 lot" is so deaf**

As in algebra, we understand that

**Do not confuse addition and multiplication laws**

\[\sqrt{3}+\sqrt{3}=2 \sqrt{3}\]

\[\sqrt{3} \times \sqrt{3}=\sqrt{9}=3\]

Algebra reference knowledge to help:

^{2}

**Do not fully simplify each surd**

As in the example

**Trying to match as opposed to surds**

It's okay to leave an answer with more than one deaf unless it's further simplified.

Adding and subtracting surdos is part of our series of lessons to support repeating surdos. It can be helpful to start with the main lesson to get a summary of what to expect, or use the step-by-step instructions below for more detail on individual topics. Other lessons in this series include:

- deaf
- rationalize the denominator
- simplified deaf
- Multiply and divide deaf
- Simplified Deaf

### Practice adding and subtracting voiceless questions

1. Simplify:

3 \sqrt{11}+2 \sqrt{11}-\sqrt{11}

6 \sqrt{11}

4 \sqrt{11}

7 \sqrt{11}

5 \sqrt{11}

Already in a similar way;3+2-1=4.

2. Simplify:

3\sqrt{5}-2\sqrt{3}+4\sqrt{3}

3 \sqrt{5}+2 \sqrt{3}

5 \sqrt{15}

-24 \sqrt{15}

3 \sqrt{5}-2 \sqrt{3}

We can only collect Like root3S;4-2=2.

3. Simplify:

\sqrt{11}+\sqrt{44}

5\sqrt{11}

\sqrt{55}

3\sqrt{11}

11 \sqrt{5}

4is a square factor of44, then use this to simplify the root44. There is then a root similar to the root11.

4. Simplify:

\sqrt{54}-\sqrt{24}

\sqrt{30}

6\sqt{30}

6\sqt{6}

\sqrt{6}

9is a square factor of54E4is a square factor of24. If you simplify both roots, there will be a root similar to root6.

5. Simplify:

3\sqrt{20}-\sqrt{50}

3\sqrt{1000}

6-\sqrt{10} \sqrt{5}

6\sqrt{5}-5\sqrt{2}

6\sqrt{10} \sqrt{5}

If both surds are fully simplified, they won't be like surds. We simply write the result as a subtraction using simplified surdos.

6. Simplify:

3 \sqrt{16}+\sqrt{50}-\sqrt{8}

12+5 \sqrt{10}-2 \sqrt{2}

12+3 \sqrt{2}

\sqrt{2}(3+3 \sqrt{8})

12-3 \sqrt{2}

Root 16 is not deaf so let's work it out3\eggs4=12. So if you look at the surdos, if they're both simplified, there's a similar surd from the root2. We combine these two deaf.

### Adding and Subtracting Deaf GCSE Questions

1. express\sqrt{6}+\sqrt{54}in shapea \sqrt{6}WoAis an integer.

**(2 points)**

show the answer

\sqrt{54}=\sqrt{9} \times \sqrt{6}

**(1)**

\sqrt{6} + \sqrt{54} =4\sqrt{6}(a=4)

**(1)**

2. Completely Simplify\sqrt{32}+\sqrt{2}

**(2 points)**

show the answer

\sqrt{32}=\sqrt{16} \times \sqrt{2}

**(1)**

5 \sqrt{2}

**(1)**

3. Writing\sqrt{40}+\sqrt{160}in shapea \sqrt{10}

**(3 points)**

show the answer

\sqrt{40}=\sqrt{4} \times \sqrt{10}

**(1)**

\sqrt{160}=\sqrt{16} \times \sqrt{10}

**(1)**

\sqrt{40} + \sqrt{160} =6\sqrt{10}(a=6)

**(1)**

## learn checklist

Now you've learned how to:

- Add and subtract deaf

## The next classes are

- Repeating decimals in fractions
- Compare fractions, decimals and percentages
- square numbers and square roots

## Still stuck?

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