Find the length of the 3rd side of each right triangle.
1. 8^2+15^2=c^2 Answer: c=17
2. 5^2+b^2=13^2 Answer: b=12
3. 9^2+13^2=c^2 Answer: c~15.81
Simplify. Assume that all variables are nonnegative.
{ this means square root
4. {12 Answer: 2{3
5. 2{75 Answer: 10{3
6. -3{72 Answer: -18{2
7. {200 Answer: 10{2
8. {3x^2 Answer: 3x
9. {3{18 Answer: 3{6
10. {5{10 Answer: 5{2
11. {15{6 Answer: 3{10
12. {3{27 Answer: 9
13. {18{14x Answer: 6{7x
14. {12{18 Answer: 6{6
15. {2/{5 Answer: {10/5
16. {75/{15 Answer: {5
17. 2/{2 Answer: {2
18. {9/{100 Answer: 3/10
19. -{49/{100 Answer: -7/10
20. {27/{75 Answer 3/5
If I get any of these wrong, can someone please show me how to them correctly ?
good job, I agree with all of them
1,2,3,4,5,6,7 are ok.
8. sqrt (3x^2) = x*sqrt(3) Check that.
9,10,11 ok.
12.
sqrt(3)*sqrt(27) = sqrt 3*sqrt(3*9)
9*sqrt(9) = 9*3= 27. Check that.
check 15. I think you just wrote it wrong. I get 1/5*sqrt(10). Check that.
The others look ok.
I goofed on 12. It's ok.
Thank you both!
I agree with DrBob
I should have checked them a bit less superficially.
Sure! Let's go through each question step by step.
1. To find the length of the third side of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we have: 8^2 + 15^2 = c^2, where c is the length of the third side.
Solving the equation, we get: 64 + 225 = c^2, which simplifies to 289 = c^2.
Taking the square root of both sides, we get c = √289, which gives us c = 17.
2. Again, we can use the Pythagorean theorem: 5^2 + b^2 = 13^2. So we have 25 + b^2 = 169.
Simplifying, we get b^2 = 144, and taking the square root of both sides gives us b = √144, which is 12.
3. Applying the Pythagorean theorem once more: 9^2 + 13^2 = c^2. So we have 81 + 169 = c^2, which simplifies to 250 = c^2.
Taking the square root of 250, we get c ≈ √250 ≈ 15.81.
Now let's move on to the simplifying problems.
4. To simplify √12, we need to find the largest perfect square that divides evenly into 12. In this case, it is 4, because 4 * 3 = 12.
Therefore, we can rewrite √12 as √(4 * 3), which simplifies to √4 * √3.
Since √4 = 2, the answer is 2√3.
5. In √75, we look for the largest perfect square that divides evenly into 75. It is 25, because 25 * 3 = 75.
So we can rewrite √75 as √(25 * 3), which simplifies to √25 * √3.
Since √25 = 5, the answer is 5√3.
6. For √72, we find the largest perfect square that divides evenly into 72. It is 36, because 36 * 2 = 72.
Thus, √72 can be simplified as √(36 * 2), which becomes √36 * √2.
Since √36 = 6, the answer is 6√2.
Continue this process for the remaining problems, and let me know if you need any further explanations or assistance with specific questions.