Solve this surd
Root 147/4 divided by Root 27/2.
well, (147/4) / (27/2) = 147/4 * 2/27 = 49/9 * 1/2
so √(147/4) / √(27/2) = √(49/9 * 1/2) = (7/3)/√2 = 7/(3√2) or 7√2/6
sqrt [ (147/4) / (54/4) ] ????
=sqrt (147/4)
= (1/2) sqrt (147)
= (1/2) sqrt (49 * 3)
= (7/2) sqrt 3
Sorry to ask...
Please how did you get (1/2)
To solve this surd, we can simplify the expression by applying the rules of surds:
√(147/4) / √(27/2)
First, let's simplify the numbers inside the square roots:
√(147/4) = √(147) / √(4)
√(27/2) = √(27) / √(2)
Now, let's simplify the square roots of these numbers:
√(147) = √(3 * 49) = 7√3
√(4) = 2
√(27) = √(3 * 9) = 3√3
√(2) = √2
Now, substitute these values back into the original expression:
(7√3 / 2) / (3√3 / √2)
To divide by a fraction, we can multiply by its reciprocal:
(7√3 / 2) * (√2 / 3√3)
Now, let's simplify this expression by canceling out common factors:
(7 * √2 * √3) / (2 * 3 * √3 * √3)
√3 * √3 simplifies to 3:
(7 * √2 * 3) / (2 * 3 * 3)
Simplify further:
(7 * √2) / (2 * 3)
Now, cancel out common factors:
7/2 * √2/3
Therefore, the simplified form of the expression is:
7√2 / 6