My question involves "Graphic Representation of Radicals of the Second Order" I know that the length of the hypotneuse of a right triangle equals the square root of the sum of the lengths of the two legs. The problems I'm having trouble with are the square roots of 15, 24, 34. Theres also one with 1/2 in front of the square root of 5. THis is all Greek to me. Can u help me??

Certainly! I can help you with understanding the square roots of 15, 24, 34, and 1/2√5, as well as how to represent them graphically.

To start, let's review square roots. The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4*4 equals 16.

Now, let's look at the square roots of the numbers you mentioned.

1) Square root of 15: This is an irrational number, which means it cannot be expressed as a fraction or a terminating decimal. To approximate its value, you can use a calculator or find the nearest whole numbers whose squares are higher and lower than 15. In this case, the square root of 15 is approximately 3.873.

2) Square root of 24: Similar to the previous example, you can approximate the square root of 24. It is approximately 4.899.

3) Square root of 34: Again, you can approximate the square root of 34. It is approximately 5.830.

Now, let's discuss how to represent square roots graphically. In a right triangle, the square roots of the lengths of the two shorter sides can be thought of as the lengths of those sides themselves. For example, if the two shorter sides of a right triangle are 9 and 16, then their square roots are 3 and 4. These values represent the actual lengths of the sides.

For the case of 1/2√5, it means taking half of the square root of 5. First, find the square root of 5 which is approximately 2.236. Then, take half of that value, which gives you approximately 1.118.

In conclusion, to better understand the square roots of 15, 24, 34, and 1/2√5, you can approximate their values using calculators or by finding the nearest whole numbers. Graphically, the square roots represent the actual lengths of the sides in a right triangle.