Rationalize the denominator and simplify...
radical 44x^2/radical 11 +3
Help would be appreciated :)
you have
2x√11/(√11+3)
multiply by √11-3 up and down:
2x√11(√11-3)/(√11+3)(√11-3)
(2x*11 - 6x√11)/(11 - 9)
(22x - 6x√11)/2
11x - 3√11 x
To rationalize the denominator and simplify the expression, we will follow a few steps:
Step 1: Start by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of a binomial is obtained by changing the sign between the two terms. In this case, the denominator is "√11 + 3," so the conjugate will be "√11 - 3."
Step 2: Multiply the numerator and denominator by the conjugate:
[(√44x^2) * (√11 - 3)] / [(√11 + 3) * (√11 - 3)]
Step 3: Simplify the numerator:
√(44x^2) can be broken down as √(4 * 11 * x^2), which simplifies to 2x√11.
Therefore, the numerator becomes 2x√11 * (√11 - 3).
Step 4: Multiply the denominator:
(√11 + 3) * (√11 - 3) can be simplified using the difference of squares formula, which states that (a - b)(a + b) = a^2 - b^2. In this case, a = √11 and b = 3. So the denominator becomes (√11)^2 - (3)^2 = 11 - 9 = 2.
Step 5: Simplify the expression:
The simplified expression becomes:
(2x√11 * (√11 - 3)) / 2
Step 6: Cancel out the common factor of 2:
2x√11 * (√11 - 3) is divided by 2, so the expression simplifies to:
x√11 * (√11 - 3)