Multiply
(5sqrt5-10sqrt 6)* (3sqrt5+6sqrt6)
give it a shot,
use FOIL and the fact that √a * √b = √(ab)
thanks so much!!
To multiply the given expressions (5√5 - 10√6) * (3√5 + 6√6), we will expand using the distributive property.
First, let's multiply the terms in the first parentheses by the terms in the second parentheses:
(5√5 - 10√6) * (3√5 + 6√6)
= 5√5 * 3√5 + 5√5 * 6√6 - 10√6 * 3√5 - 10√6 * 6√6
= 15(√5 * √5) + 30(√5 * √6) - 30(√6 * √5) - 60(√6 * √6)
Next, we simplify the square roots in each term:
= 15(√(5*5)) + 30(√(5*6)) - 30(√(6*5)) - 60(√(6*6))
= 15(√25) + 30(√30) - 30(√30) - 60(√36)
= 15(5) + 0 - 0 - 60(6)
= 75 - 360
= -285
Therefore, the final answer is -285.
To multiply the given expression, we can use the distributive property of multiplication over addition.
First, let's break down the expression into two parts:
Part 1: (5√5)(3√5)
To multiply two expressions with radicals, we multiply the coefficients and multiply the radicals. In this case, 5 and 3 are the coefficients, and √5 and √5 are the radicals.
5 * 3 = 15
√5 * √5 = 5
So, (5√5)(3√5) = 15√5
Part 2: (5√5)(6√6)
Similarly, we multiply the coefficients and multiply the radicals.
5 * 6 = 30
√5 * √6 = √30
So, (5√5)(6√6) = 30√30
Now, let's combine the two parts:
(5√5 - 10√6)(3√5 + 6√6) = (15√5 - 30√6)(3√5 + 6√6)
Using the distributive property, we multiply each term in the first bracket by each term in the second bracket:
= (15√5 * 3√5) + (15√5 * 6√6) - (30√6 * 3√5) - (30√6 * 6√6)
Simplifying further:
= 15 * 3 * (√5 * √5) + 15 * 6 * (√5 * √6) - 30 * 3 * (√6 * √5) - 30 * 6 * (√6 * √6)
= 45 * 5 + 90√30 - 90√30 - 180 * 6
= 225 + 0 - 1080
= -855
Therefore, the result of the expression (5√5-10√6)(3√5+6√6) is -855.