divide and simplify the radical
(3+ sqrt18)/4 sqrt12
I'm not sure how to conjugate the denominator?
repartir 152 entre A,B,C de modo que la parte de B sea 8 menos que el duplo de la de A y 32 mas que la de C
(3+√18) / 4√12
= (3+3√2) / 8√3
= 3√3 (1+√2) / 24
= (1+√2)√3 / 8
= (√3+√6)/8
or several other ways to express it
B = 2A-8
B = C+32
A+B+C = 152
C = B-32 = 2A-8-32
A + 2A-8 + 2A-40 = 152
5A - 48 = 152
5A = 200
A=40
B=72
C=40
To divide and simplify the given expression (3+√18) / (4√12), we need to rationalize the denominator to eliminate any radicals.
Rationalizing the denominator involves multiplying both the numerator and denominator by a suitable expression that eliminates the radical in the denominator. In this case, we will multiply by the conjugate of the denominator to achieve that.
The conjugate of the denominator, 4√12, is obtained by changing the sign of the radical. So, the conjugate is -4√12.
To rationalize the denominator and divide the expression, we follow these steps:
Step 1: Multiply both the numerator and denominator by the conjugate of the denominator.
(3+√18) / (4√12) * (-4√12) / (-4√12)
Step 2: Simplify the numerator by applying the distributive property.
(-4√12 * 3) + (-4√12 * √18)
-12√12 - 4√(12*18)
-12√12 - 4√216
Step 3: Simplify each radical term.
-12√12 - 4√(36*6)
-12√12 - 4√36√6
-12√12 - 4 * 6√6
-12√12 - 24√6
Step 4: Combine like terms (if any).
-12√12 - 24√6 (There are no like terms to combine in this case.)
And that's the simplified form of the expression (3+√18) / (4√12).