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maths - Coggle Diagram
maths
surds
rules
square root of m divided by square root of n = square root of m over n
√m / √n = √m / n
square root of m times square root of n = square root of mn
√m x √n = √mn
you cant add surds which dont have the same "denominator"
2√27 + 3√3
2√27 = 2 x 3√3 = 6√3
6√3 + 3√3 = 9√3
you cant add these because 27 is not 3. however you can simplify surds
√90 = √9 x √10 = 3√10
√32 = √16 x √2 = 4√2
√54 = √9 x √6 = 3√6
simplifying surds
sqrt{5}
(
sqrt{8} + sqrt{18}
)
factorise = sqrt{40} + sqrt{90}
(5 x 8 is 40 and 5 x 18 is 90)
sqrt{4 x 10} + sqrt{9 x 10}
2sqrt{10} + 3sqrt{10}
5sqrt{10}
a = 5
when this equation is written as
a
(sqrt{10}), find
a
3 = √9 so (√9 x √3)²
= (√27)²
= 27
√3 x √3 = 3
√3 x 1 = √3
√3 x -1 = -√3
-1 x 1 = -1
√3 + -√3 = 0
0 + 3 + -1 = 2
rationalising surds
√5 x √5 is 5, and 5 + 2 = 7
symbols
√
²
