Surds

Question 1

Simplifying Surds

Answer 1

Find a square number that is a factor of the number under the root.

Rewrite the surd as a product of this square number and another number, then evaluate the root of the square number.

Repeat if the number under the root still has square factors.

√8 can be written as √4×√2, which equals 2√2

10√8 = 4sqrt(5)

Question 2

Adding and Subtracting Surds

Answer 2

The rule for adding and subtracting surds is that the numbers inside the
square roots
must be the same.

5sqrt(2) - 3sqrt(2) = 2sqrt(2)

5sqrt(3) - 1sqrt(4) = won’t work since the numbers inside the sqrt are not the same

Question 3

Multiplying / Dividing Surds

Answer 3

The sqrt of something timed by itself is the number
Example; sqrt(5) x sqrt(5) = 5

Sqrt(8) x sqrt(10) = sqrt(80)
Sqrt(80) = sqrt(16x5) = 4 x sqrt(5) = 4sqrt(5)

2sqrt(3) x 3sqrt(2)

Multiply the whole numbers
2x3 = 6
Multiply the surds
Sqrt(3) x sqrt(2) = sqrt(6)

So the answer is 6sqrt(6)

Question 4

Simplify √12

Answer 4

12 = 4x3
Sqrt(12) = sqrt ( (4x3) ) = sqrt(4) x sqrt(3)
Sqrt(4) = 2
So sqrt(12) = 2sqrt(3)

Question 5

Simplify sqrt(8)

Answer 5

8 = 4x4
Sqrt(8) = sqrt ( (4x4) ) = sqrt(4) x sqrt(4)
Sqrt(4) = 2
So sqrt(8) = 2sqrt(2)

Question 6

Simplify sqrt(12)/sqrt(6)

Answer 6

Sqrt(12)/sqrt(6) = sqrt(12/6)

12/6 = 2

Sqrt(12)/sqrt(6) = sqrt(2)

Question 7

Add 7sqrt(4) + 9sqrt(4)

Answer 7

7sqrt(4) + 9sqrt(4) = 16sqrt(4)

This simplify to 4sqrt(4)

Question 8

Subtract 5sqrt(2) - 2sqrt(2)

Answer 8

5sqrt(2) - 2sqrt(2) = 3sqrt(2)

This cannot be simplified