Simplify
8.3^1/2 /( 6^1/2 + 5^1/2)
To simplify the expression 8.3^(1/2) / (6^(1/2) + 5^(1/2)), we need to evaluate the square roots and perform the indicated operations.
Step 1: Evaluate the square roots
The square root of 8.3 is approximately 2.88 because √8.3 ≈ 2.88.
The square root of 6 is exactly √6.
The square root of 5 is exactly √5.
Step 2: Substitute the square roots
Now we substitute these values back into the expression:
2.88 / (√6 + √5)
Step 3: Rationalizing the denominator
To simplify the expression further, we need to remove the radicals from the denominator by rationalizing it. To do this, we multiply the numerator and denominator by the conjugate of the denominator, which is (√6 - √5) because the product of a binomial and its conjugate is a difference of squares.
(2.88 / (√6 + √5)) * ((√6 - √5) / (√6 - √5))
Simplifying this gives us:
(2.88 * (√6 - √5)) / ((√6 + √5) * (√6 - √5))
Since (√6 - √5) * (√6 + √5) = (√6)^2 - (√5)^2 = 6 - 5 = 1, our expression simplifies to:
(2.88 * (√6 - √5)) / 1
Finally, the simplified expression is:
2.88 * (√6 - √5)