Question

What is the value of x? Leave your answer in simlplest radical form.

Answer 1

Using pythagoras theorem,

`{ c}^(2) = {a}^(2) + {b}^(2) \\ {x}^(2) = {3}^(2) + {3}^(2) \\ {x}^(2) = 18 \\ x = √(18)`
Now we know that the answer is root 18, we can simplify this to a radical:

`√(18) = √(9) * √(2) \\ √(18) = 3 * √(2) \\ √(18) = 3 √(2)`
So our answer is 3 root 2

Answer 2

Using the Pythagorean theorem,
.. x^2 = 3^2 +3^2 = (3^2)*2
.. x = √((3^2)*2)
.. x = 3√2 . . . . . . . . matches selection (a)

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The hypotenuse of an isosceles right triangle is always √2 times the length of either leg. Since the legs are 3, the hypotenuse is 3√2. You only need to remember this fact to save a bunch of arithmetic.