Simplify $\frac{\sqrt{72}}{\sqrt{10} \cdot \sqrt{2} \cdot \sqrt{3} \cdot \sqrt{5}}$. Your answer should have an integer denominator.
+2666 Simplify the denominator to: \(\sqrt{10 \times 2 \times 3 \times 5} = \sqrt{300} = 10 \sqrt 3\)
Now, simplify the numerator to: \(\sqrt{72} = 6 \sqrt 2\)
This means that the new fraction is: \({{ 6 \sqrt 2} \over {10 \sqrt 3 }} = {3 \sqrt 2 \over 5 \sqrt 3}\)
However, we need to rationalize the denominator by multiplying the fraction by \({5 \sqrt 3 } \over 5 \sqrt 3\). This will make the denominator an integer.
Can you take it from here?
+2666 Simplify the denominator to: \(\sqrt{10 \times 2 \times 3 \times 5} = \sqrt{300} = 10 \sqrt 3\)
Now, simplify the numerator to: \(\sqrt{72} = 6 \sqrt 2\)
This means that the new fraction is: \({{ 6 \sqrt 2} \over {10 \sqrt 3 }} = {3 \sqrt 2 \over 5 \sqrt 3}\)
However, we need to rationalize the denominator by multiplying the fraction by \({5 \sqrt 3 } \over 5 \sqrt 3\). This will make the denominator an integer.
Can you take it from here?
