Question

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

Answer 1

Using pythagoras theorem,
${ c}^{2} = {a}^{2} + {b}^{2} \\ {x}^{2} = {3}^{2} + {3}^{2} \\ {x}^{2} = 18 \\ x = \sqrt{18}$
Now we know that the answer is root 18, we can simplify this to a radical:
$\sqrt{18} = \sqrt{9} \times \sqrt{2} \\ \sqrt{18} = 3 \times \sqrt{2} \\ \sqrt{18} = 3 \sqrt{2}$
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.