divide 2√3 / √5−3√2
To solve this problem, we will need to rationalize the denominator.
First, let's take the conjugate of the denominator: √5 + 3√2.
Now, to rationalize the denominator, we multiply both the numerator and denominator by the conjugate.
(2√3 / √5−3√2) * (√5 + 3√2) / (√5 + 3√2)
Expanding this, we get:
(2√3 * √5 + 2√3 * 3√2) / (√5 * √5 + √5 * 3√2 - 3√2 * √5 - 3√2 * 3√2)
Simplifying, we get:
(2√15 + 6√6) / (5 + 3√10 - 3√10 - 18)
Combining like terms, we have:
(2√15 + 6√6) / (-13)
Therefore, the simplified answer is:
-(2√15 + 6√6) / 13
To divide the expression 2√3 / (√5 - 3√2), we need to rationalize the denominator.
Step 1: Start by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of √5 - 3√2 is √5 + 3√2.
(2√3 / (√5 - 3√2)) * (√5 + 3√2 / √5 + 3√2)
Step 2: Simplify the numerator and denominator.
Numerator: (2√3) * (√5 + 3√2) = 2√15 + 6√6
Denominator: (√5 - 3√2) * (√5 + 3√2) = (√5)^2 - (3√2)^2 = 5 - 9(2) = 5 - 18 = -13
Step 3: Rewrite the division as multiplication by the reciprocal.
(2√15 + 6√6) / (-13)
So, the final simplified expression is (2√15 + 6√6) / (-13).
To simplify the expression (2√3) / (√5 - 3√2), we need to rationalize the denominator. Rationalizing the denominator means eliminating any radicals (square roots) in the denominator.
Here are the steps to rationalize the denominator in this case:
1. Multiply both the numerator and denominator of the expression by the conjugate of the denominator. The conjugate of √5 - 3√2 is √5 + 3√2.
(2√3) / (√5 - 3√2) * (√5 + 3√2) / (√5 + 3√2)
2. Simplify the numerator and denominator separately.
Numerator: (2√3) * (√5 + 3√2) = 2√3 * √5 + 6√6 = 2√15 + 6√6
Denominator: (√5 - 3√2) * (√5 + 3√2) = (√5)^2 - (3√2)^2 = 5 - 9(2) = 5 - 18 = -13
3. Simplify the whole expression by dividing the numerator by the denominator.
(2√3) / (√5 - 3√2) * (√5 + 3√2) / (√5 + 3√2) = (2√15 + 6√6) / (-13)
So, the simplified expression is (2√15 + 6√6) / -13.