Radicals
- Thread starter Catelyn04
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Are you supposed to leave the answers as radicals?
Are you supposed to use calculator?
Some extra information which may help you when working with surds:
To simplify a surd you need to know how to multiply surds and how to break a larger surd down to a multiple of a smaller surd.
Multiplying a surd by a surd works the same way as whole numbers:
2 × 3 = 6 √2 × √3 = √6
3 × 3 = 9 √3 × √3 = √9 √9 = 3 since 3² = 9 (square number)
Multiplication of surds with letters works the same way as surds involving numbers except with numbers the expression inside the square root sign is evaluated.
√a × √b = √(a × b) = √ab √3 × √5 = √(3 × 5) = √15
Multiplying a surd by a number works the same way as multiplying a letter by a number:
2 × a = 2a (2a = a + a)
2 × √3 = 2√3 (2√3 = √3 + √3)
2 × √a = 2√a (2√a = √a + √a)
Examples:
Simplify √16
4 × 4 = 16 (square number)
√16 = √(4 × 4)
= 4
Similarly √(a²) = a where a = 4 (notice how the square symbol cancels with the square root because these are inverse operations).
Simplify √48
We break the surd down by looking for a square number (in this case 16) which divides into 48 with no remainder.
√48 = √(16 × 3)
= √16 × √3
= 4√3
Simplify √275
√275
= √(25 × 11)
= √25 × √11
= 5√11
Simplify √6 + 2√6 - 5 √6
√6 + 2√6 - 5 √6
= 3 √6 - 5√6
= -2√6
Similarly b + 2b - 5b = -2b where b = √6
To simplify a surd you need to know how to multiply surds and how to break a larger surd down to a multiple of a smaller surd.
Multiplying a surd by a surd works the same way as whole numbers:
2 × 3 = 6 √2 × √3 = √6
3 × 3 = 9 √3 × √3 = √9 √9 = 3 since 3² = 9 (square number)
Multiplication of surds with letters works the same way as surds involving numbers except with numbers the expression inside the square root sign is evaluated.
√a × √b = √(a × b) = √ab √3 × √5 = √(3 × 5) = √15
Multiplying a surd by a number works the same way as multiplying a letter by a number:
2 × a = 2a (2a = a + a)
2 × √3 = 2√3 (2√3 = √3 + √3)
2 × √a = 2√a (2√a = √a + √a)
Examples:
Simplify √16
4 × 4 = 16 (square number)
√16 = √(4 × 4)
= 4
Similarly √(a²) = a where a = 4 (notice how the square symbol cancels with the square root because these are inverse operations).
Simplify √48
We break the surd down by looking for a square number (in this case 16) which divides into 48 with no remainder.
√48 = √(16 × 3)
= √16 × √3
= 4√3
Simplify √275
√275
= √(25 × 11)
= √25 × √11
= 5√11
Simplify √6 + 2√6 - 5 √6
√6 + 2√6 - 5 √6
= 3 √6 - 5√6
= -2√6
Similarly b + 2b - 5b = -2b where b = √6