sqrt(15)/5 *sqrt(20)
so if you mean: \(\frac{ \sqrt{15} }{5}\) times \(\sqrt{20}\) then
simplify
rememeber
\(x^{ \frac{m}{n} }= \sqrt[n]{ x^{m} }\)
and
\([x^{n}]^{m}= x^{nm}\)
and
\(\sqrt{x} \sqrt{y}= \sqrt{xy}\)
multiply
\(\frac{ \sqrt{15} }{5}\) times \(\frac{ \sqrt{20} }{1}\)=\(\frac{ \sqrt{300}}{5}\)
simplify √300
√300=√3 times √100
we know that √100=10 so
√300=√3 times 10
therefor
\(\frac{ \sqrt{300} }{5}\) = \(\frac{10\sqrt{3}}{5}\)= \(\frac{5}{5}\) times \(\frac{2\sqrt{3}}{1}\) = 1 times \(\frac{2\sqrt{3}}{1}\)=2√3
So,
\(\frac{ \sqrt{15}}{5} * \sqrt{20}\)
Simplify the square root of 20.
\(\sqrt{20} = \sqrt{4} * \sqrt{5} = 2 * \sqrt{5} = 2 \sqrt{5}\)
\(\frac{ \sqrt{15}}{5} * \frac{ 2\sqrt{5} }{1}\)
Multiply.
\(\frac{ 2\sqrt{75}}{5}\)
Simplify.
\(\frac{ 2\sqrt{25}* \sqrt{3} }{5}\)
\(\frac{ 2 * 5* \sqrt{3} }{5}\)
\(\frac{10\sqrt{3} }{5}\)
\(\frac{2\sqrt{3} }{1}\)
\(2\sqrt{3}\)