Addition and subtraction with radicals

*NB: You can only add and subtract radicals if they are the same.
√<---- this is the radical sign just incase anyone is wondering.

Ex. √3 + √2=√3 + √2
√3 + √3 =2√3 <---because the radical is the same. Therefore, they can be combined.

Try: 1) 2√5+ 3√5 + 6√5=11√5
2) 5√7 +3√7-2√7=6√7


-What if the radical is different?

Ex. √12 + √18 - √27 + √8
Step one: Simplify if you can.

√12 √18 √27 √8
4x3 9x2 9x3 4x2 <----the first number always has to be a square root.
√4 x √3 + √9 x √2 + √9 x √3 + √4 x √2<---square root the first number.
2√3 + 3√2 - 3√3 + 2√2
Step two: Combine like terms.
2√3 - 3√3 +3√2 +2√2
-1√3 + 5√2

Ex. √12 + 2√8 -3√75 + √2
4x3 2√4x2 3√25x3 √2
√4 x √3 + 2√4 x √2 -3√25 x √3 + √2
2√3 + 2x2√2 - 3x5√3 + √2
2√3 + 4√2 - 15√3 + √2
=-13√3 + 5√2

Try: 1) √12 + √27
4x3 9x3
√4 x √3 + √9 x √3
2√3 + 3√3
= 5√3

2) √28 - √27 +√63 + √300
4x7 9x3 9x7 100x3
√4 x √7 - √9 x √3 + √9 x √7 + √100 x √3
2√7 - 3√3 + √3 x √7 + √10 x √3
= 5√7 + 7√3

Exercise # 34
Questions 1-9, 11, 13, 14

the next person to scribe is going to be..Katherine