Simplify (√98 -√50)/√32
The correct answer is C. 1/2
Let's simplify the given expression step by step:
\(\frac{\sqrt{98} - \sqrt{50}}{\sqrt{32}}\)
First, let's simplify the square roots:
\(\sqrt{98} = \sqrt{49 \cdot 2} = \sqrt{49} \cdot \sqrt{2} = 7\sqrt{2}\)
\(\sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}\)
\(\sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}\)
Now, substitute these values back into the original expression:
\(\frac{7\sqrt{2} - 5\sqrt{2}}{4\sqrt{2}}\)
Simplify the numerator:
\(2\sqrt{2}\)
Now, substitute the simplified numerator back into the expression:
\(\frac{2\sqrt{2}}{4\sqrt{2}}\)
Simplify by canceling out the common factor:
\(\frac{2}{4}=frac{1}{2}\)
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