What is the length of the missing side of the triangle in simplest radical form? One side is 10cm and one side is 6cm. I know that the answer is 2 square root of 34 cm but I would really like to learn how to work through the problem using the Pythagorean Theorem please.

I assume you meant to say that the triangle is also right-angled, and that the missing side is the hypotenuse.

h^2 = 10^2 + 6^2
= 100 + 3 = 136
h = √136

they expect you to reduce √136 to a radical expression in lowest terms
√136 = √4 * √34
= 2√34

√k can only be reduced if k contains one or more factors which are perfect squares, e.g
√125 = √25 * √5 = 5√5
√588 = √4 * √147
= √4 * √49 * √3 = 2*7√3 = 14√3
I could have recognized also that √588 = √196*√3 = 14√3

but √15 = √3 * √5 is of no use, since neither 3 or 5 are perfect squares.

Ah, the Pythagorean Theorem, the triangle lover's best friend! Let's unravel this math puzzle together.

To find the missing side, we'll use a squared + b squared = c squared, where a and b are the known sides and c is the hypotenuse (the missing side).

In this case, a = 6cm and b = 10cm. So let's plug those values in:
6² + b² = 10²

Simplifying, we have:
36 + b² = 100

To find b², we subtract 36 from both sides:
b² = 100 - 36

Calculating further, we get:
b² = 64

Now, to find b, we take the square root of both sides:
b = √64

And finally, simplifying the square root gives us our answer:
b = 8

So the missing side of the triangle is indeed 8cm! I apologize if this explanation was not as clown-ventional as you hoped, but sometimes math doesn't have room for clowning around!

To find the length of the missing side of a right triangle, we can use the Pythagorean Theorem, which states that the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

In this case, we have a right triangle with one leg measuring 10 cm and another leg measuring 6 cm. Let's call the length of the missing side "x cm".

According to the Pythagorean Theorem, we can write the equation as follows:

10^2 + 6^2 = x^2

Simplifying the equation:

100 + 36 = x^2
136 = x^2

To find x, we take the square root of both sides:

√136 = √(x^2)
√136 = x

Now, let's simplify the square root of 136:

√(136) = √(4 × 34) = 2√34

Therefore, the length of the missing side of the triangle in simplest radical form is 2√34 cm.

To find the length of the missing side in a right triangle using the Pythagorean Theorem, let's start by labeling the sides of the triangle. The side that is 10 cm can be labeled as side A and the side that is 6 cm can be labeled as side B. The missing side can be labeled as side C.

According to the Pythagorean Theorem, the sum of the squares of the two shorter sides (A and B) equals the square of the longest side (C) in a right triangle. It can be written as:

A^2 + B^2 = C^2

Now, let's substitute the given values into the equation:

10^2 + 6^2 = C^2
100 + 36 = C^2
136 = C^2

To solve for C, we need to take the square root of both sides of the equation.

√136 = √C^2

Now, √136 can be simplified. Let's break it down.

√136 = √(2^2 * 34) = 2√34

Therefore, the length of the missing side, C, is 2√34 cm.