I need some help figuring these.

Compute each product and simplify the result. I don't have the squareroot sign so put that meaning that's where it goes with the number after it.

1. (0.3 Squareroot of 5)^2
2. (2+ squareroot of 5)^2

3. (5+4Squareroot of 10)(1-2 squareroot of 10)

4. (3 squareroot 5 + 4 squareroot 2)(squareroot 15+ squareroot 6)

To solve these problems, we need to simplify each expression by performing the indicated operations. Here's how you can solve each one:

1. (0.3 √5)^2
To square a number, we multiply it by itself. So, we square 0.3 and √5 separately and then multiply them together.
0.3^2 = 0.09 (square of 0.3)
(√5)^2 = 5 (square of √5)
Now, multiply the results together:
0.09 * 5 = 0.45
So, the product is 0.45.

2. (2 + √5)^2
To square a binomial expression, we can use the formula (a + b)^2 = a^2 + 2ab + b^2.
In this case, a = 2 and b = √5.
(a^2) = (2)^2 = 4
(b^2) = (√5)^2 = 5
(2ab) = 2 * 2 * √5 = 4√5
Now, substitute these values in the formula:
(2 + √5)^2 = 4 + 4√5 + 5 = 9 + 4√5
So, the simplified result is 9 + 4√5.

3. (5 + 4√10)(1 - 2√10)
To multiply these binomial expressions, we can use the distributive property. Multiply each term of the first expression by each term of the second expression.
(5 * 1) = 5
(5 * -2√10) = -10√10
(4√10 * 1) = 4√10
(4√10 * -2√10) = -8√10 * √10 = -8 * 10 = -80
Now, combine the like terms:
5 - 10√10 + 4√10 - 80
(-10√10 + 4√10) can be simplified as (-10 + 4)√10 = -6√10.
So, the simplified result is 5 - 6√10 - 80 = -75 - 6√10.

4. (3√5 + 4√2)(√15 + √6)
Again, using the distributive property, we multiply each term of the first expression by each term of the second expression.
(3√5 * √15) = 3√(5 * 15) = 3√75
(3√5 * √6) = 3√(5 * 6) = 3√30
(4√2 * √15) = 4√(2 * 15) = 4√30
(4√2 * √6) = 4√(2 * 6) = 4√12
Now, combine the like terms (which means simplifying the square roots):
3√75 + 3√30 + 4√30 + 4√12
We can simplify the square roots using factors:
3√75 = 3√(25 * 3) = 3 * 5√3 = 15√3
3√30 + 4√30 = √30(3 + 4) = 7√30
4√12 = 4√(4 * 3) = 4 * 2√3 = 8√3
Now, combine the simplified terms:
15√3 + 7√30 + 8√3
The result cannot be simplified any further since there are no like terms to combine.

Hope this helps you solve these problems!