Question

(√3-√5)корень из (8+2√15)=?

Answer 1

Решение задания приложено

Answer 2

(√3-√5)*√ (8+2√15)= (√3-√5)* √ (√3²+2√(3*5) +√5²) =

= (√3-√5)*√ (√3+√5)²=

= (√3-√5)* (√3+√5)= √3²-√5²=3-5 = - 2

Answer 3

To simplify the expression (√3 - √5)√(8 + 2√15), we can follow these steps:

Step 1: Distribute the square root to each term inside the parentheses. Step 2: Simplify the square roots where possible.

Let's begin:

Step 1: (√3 - √5)√(8 + 2√15)

Step 2: √3 * √(8 + 2√15) - √5 * √(8 + 2√15)

Now, let's deal with each part separately:

√(8 + 2√15)

Notice that 8 + 2√15 can be factored as follows: 8 + 2√15 = 2(4 + √15)

Now, let's take the square root: √(8 + 2√15) = √[2(4 + √15)] = √2 * √(4 + √15)

Now, we'll deal with √(4 + √15):

√(4 + √15)

We can't simplify this any further, so we leave it as it is.

Now, let's put everything back together:

√3 * (√2 * √(4 + √15)) - √5 * (√2 * √(4 + √15))

= √3 * √2 * √(4 + √15) - √5 * √2 * √(4 + √15)

= √6 * √(4 + √15) - √10 * √(4 + √15)

Now, notice that both terms have a common factor, √(4 + √15):

√(4 + √15) * (√6 - √10)

Thus, (√3 - √5)√(8 + 2√15) simplifies to:

√(4 + √15) * (√6 - √10)

Please note that √(4 + √15) cannot be further simplified because it involves an addition of an irrational number (√15) within the square root.