# Addition and subtraction of deaf (2023)

GCSE Mathematics Number deaf

Here we will meet youAdd and subtract deafincluding 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.

a+a+2asimplified to4a.

So if we do something similar with surds:

Z.B.

$\sqrt{3}+\sqrt{3}+2\sqrt{3}=4\sqrt{3}$

It's the same2a+3bcannot be simplified because a and b are not like terms:

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.

## How to add and subtract deaf

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

### 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.

## Examples of deaf addition and subtraction

### Example 1: like surds, simple addition

Simplify

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

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

The number under the root sign is already3in both terms, then they share a common radicand and are like deaf.

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

$7\sqrt{5}-9\sqrt{5}+6\sqrt{5}$

The number under the root sign is already5in both terms, then they share a common radicand and are like deaf.

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

$7-9+6=4$

Then,

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

### Example 3: As opposed to surds

Simplify

$10 \sqrt{2}+4 \sqrt{11}$

The numbers under the root signs are2E11; these are not like deafs.

These deaf ones cannot be simplified any further. There are no square factors for any of them.2or11.

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

$4+6\sqrt{2}-3\sqrt{2}-\sqrt{25}$

All surd terms are like surds - all are root2. The square root of 25 is not nonsense because 25 is a square number.

We don't need to simplify the deaf.

However, the square root of25AND5(It's no surprise) so let's simplify this.

$4+6\sqrt{2}-3\sqrt{2}-5$

Combining the deaf:

$6\sqrt{2}-3\sqrt{2}=3\sqrt{2}$

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

$4-5=-1$

$3\sqrt{2}-1$

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

$\sqrt{7}+\sqrt{28}$

The numbers under the root signs are7E28; these are not like deafs.

$\sqrt{7}$

it is already fully simplified; there are no square factors of7.

$\sqrt{28}$

can be simplified because4is a square factor of28.

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

\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

$\sqrt{8}+\sqrt{72}$

The numbers under the root signs are8E72; these are not like deafs.

$\sqrt{8}$

can be simplified because4is a square factor of8.

\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 because36is a square factor of72.

\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 factors4, Then9. However, you should always make sure that the surd is fully simplified - if you had left your simplification as follows:

\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.

\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

$\sqrt{75}+\sqrt{50}$

The numbers under the root signs are75E50; these are not like deafs.

$\sqrt{75}$

can be simplified because25is a square factor of75.

\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 because25is a square factor of50.

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

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

$\sqrt{90}+\sqrt{64}-\sqrt{40}$

The numbers under the root signs are90, 64E40; these are not like deafs.
64is a square number, so this isn't really nonsense.

$\sqrt{90}$

can be simplified because9is a square factor of90.

\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}

\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 thatAreally means1a.

• 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:

a + a = 2aEa × a = a2.

• Do not fully simplify each surd

As in the example6above, if we do not completely simplify each surd, it may appear that the surds cannot be simplified to give "like surds".

• 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}

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)

\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)

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

(1)

5 \sqrt{2}

(1)

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

(3 points)

\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:

## The next classes are

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

## Still stuck?

Prepare your KS4 students for success in math GCSEs with Third Space Learning. Weekly online 1-to-1 GCSE Maths Review classes taught by experienced maths teachers.

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