write down the following surds as entire surds 1) 2 root seven 2) 2³root 3 3) 7³root 2 4) 2/5 ³root 7
Answers
Answer:
follow me and mark as brainlleast
Step-by-step explanation:
ultiplication of Surds
√5 × √15 = √75 (= 15× 5)
= √25 × √3
= 5 √3
(1 + √3)(2 - √8) [The brackets are expanded as usual]
= 2 - √8 + 2√3 - √24
= 2 - 2√2 + 2√3 - 2√6
Addition and Subtraction of Surds
Adding and subtracting surds are simple- however we need the numbers being square rooted (or cube rooted etc) to be the same.
4√7 - 2√7 = 2√7.
5√2 + 8√2 = 13√2
Note: 5√2 + 3√3 cannot be manipulated because the surds are different (one is √2 and one is √3).
However, if the number in the square root sign isn't prime, we might be able to split it up in order to simplify an expression.
Example
Simplify √12 + √27
12 = 3 × 4. So √12 = √(3 × 4) = √3 × √4 = 2 × √3.
Similarly, √27 = 3√3.
Hence √12 + √27 = 2√3 + 3√3 = 5√3