Surds

Question 1

How to simplify surds?
Eg.√ 20

Answer 1

Find factors of the number where one is a square number.
Eg. √20 —> √4 * √5
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2* √5 —> 2 √5

Question 2

How to add and subtract surds?
Use: 5√ 3 + √3 and √48-√27

Answer 2

Adding:
1) add the number before the square root —> 5+1 (it’s imaginary)=6
2)don’t change the number after the square root —>6 √3
3) if the number after the square root are different then change it so they are the same (like fractions)

Subtracting:
Same as adding basically just minus-ing instead
Eg. 1) √48–> 4 √3. √27 —> 3 √3
2) 4 √3 - 3 √3= √3

Question 3

How to multiply surds?
Eg. √12* √6

Answer 3

1) make sure to simplify the first number so they have the same square root —> √12 —> 2 √3
2) make sure to simplify the 2nd number so they have the same square root —> √6 —> 3 √3
3) multiply the numbers before the square root —> 2 * 3=6
4) multiply the numbers after the square root —> 3 * 3=9
5) put it together —> 6√9
6)simplify if possible —> 6√9 —> 6*3=18

Question 4

How to expand brackets with surds?
Use 3(√2 + 5)

Answer 4

it’s basically the same as algebra.
if any of the numbers don’t have the √ then just pretend …√ 1 as it means thee same thing and makes it easier to multiply.
If any of them don’t have a number before the √ just pretend there’s a 1

Eg. 3* √2= 3√2, 3*5=15. So the answer is 3√2+15

Question 5

How to expand double brackets with surds?
Use: (3+√2)(2-√5)

Answer 5

1)Use the grid method
2)Collect like terms
3) remember to check if any numbers can simplify into a normal number

Eg. 32= 6, 3-√5= -3√5, √22= 2√2, √2-√5= -√10

Question 6

How to divide surds?
Use 4√18 / 8√2

Answer 6

If the numbers are easy to divide (f they have no number before the square root) just divide the 2 numbers
If they are harder…
Make them into fractions
See if the numbers before the square root have a common factor —> 4/8=1/2
Divide the numbers after the square root have—> 18/2= √9 —>3
Multiply the fractions together —> 1/2*3=3/2

Question 7

How to rationalise surds?
Use 4 / √2

Answer 7

Multiply the square root to the numerator and the denominator—> 4√2=4√2. √2√2=2
See if number before the surd in the numerator and denominator have a common factor —> 4/2=2
See if number after the surd in the numerator and denominator have a common factor

The main point of rationalising surds is to make sure there isn’t a surd in the denominator

Question 8

How to rationalise surds if there’s addition or subtraction?
Use 7/√5+2

Answer 8

Same method as normal rationalising
But instead of just multiply the surd u also multiply the the other number (remember to flip the sign, so if it’s +2 it’s -2 when multiplying) —> 7/√5+2*(√5-2)/(√5+2)=7(√5-2)/(√5+2)(√5-2)
Then do the grid method for the denominator
Simplify it and put that as the denominator 7√5-14/1
Finally simplify it 7√5-14