Which of these is an irrational number?
2 answers:
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1. (2√5)/5
2. -44√7
3. 8√17
4. -6√3+12
For 1: Multiply the numerator and denominator by √5:
For 2: Simplify √112:
√112 = √(2*56) = √(2*2*28) = √(4*4*7) = 2*2√7 = 4√7
Now multiply by the -11 coefficient:
-11(4√7) = -44√7
For 3: Add the radicals as you would variables that are like terms.
For 4: Multiply by the conjugate. The conjugate of the denominator has the same values with the sign of the radical changed:
2. -44√7
3. 8√17
4. -6√3+12
For 1: Multiply the numerator and denominator by √5:
For 2: Simplify √112:
√112 = √(2*56) = √(2*2*28) = √(4*4*7) = 2*2√7 = 4√7
Now multiply by the -11 coefficient:
-11(4√7) = -44√7
For 3: Add the radicals as you would variables that are like terms.
For 4: Multiply by the conjugate. The conjugate of the denominator has the same values with the sign of the radical changed: