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)
1. 0.45
2. 4sqt5 +9
3. -6sqt10 -75
4. 13sqt3 + 7sqt30
not sure though..
because sometimes i'm making mistakes in radicals...
Sure, I can help you with these problems. Let's break them down one by one and I'll explain the steps to solve them.
1. (0.3√5)^2
To square a number and simplify, you need to multiply it by itself. So, we start by squaring 0.3√5:
(0.3√5)^2 = (0.3√5) × (0.3√5)
Now, we can multiply these two terms together:
(0.3√5) × (0.3√5) = 0.3 × 0.3 × √5 × √5
Simplifying the multiplication:
0.09 × 5 = 0.45
So, the result is 0.45.
2. (2 + √5)^2
Similar to the previous problem, we want to square the expression (2 + √5):
(2 + √5)^2 = (2 + √5) × (2 + √5)
Using the distributive property, we multiply each term of the first expression by each term of the second expression:
(2 + √5) × (2 + √5) = 2 × 2 + 2 × √5 + √5 × 2 + √5 × √5
Simplifying this multiplication:
4 + 4√5 + 4 + 5 = 13 + 4√5
Therefore, the simplified result is 13 + 4√5.
3. (5 + 4√10)(1 - 2√10)
To multiply these two expressions, we can use the distributive property:
(5 + 4√10)(1 - 2√10) = 5 × 1 + 5 × (-2√10) + 4√10 × 1 + 4√10 × (-2√10)
Simplifying this multiplication:
5 - 10√10 + 4√10 - 8 × 10
Combine like terms:
5 - 80 + (4 - 10)√10
Simplifying further:
-75 - 6√10
Thus, the simplified result is -75 - 6√10.
4. (3√5 + 4√2)(√15 + √6)
Similar to the previous problems, we use the distributive property to multiply these expressions:
(3√5 + 4√2)(√15 + √6) = 3√5 × √15 + 3√5 × √6 + 4√2 × √15 + 4√2 × √6
Simplifying this multiplication:
3√(5 × 15) + 3√(5 × 6) + 4√(2 × 15) + 4√(2 × 6)
Simplifying further:
3√75 + 3√30 + 4√30 + 4√12
Now, we can combine like terms:
3√75 + 7√30 + 4√12
Therefore, the simplified result is 3√75 + 7√30 + 4√12.
I hope that helps! Let me know if you have any further questions.