maths

$\frac{\sqrt{27}\times\sqrt{50}}{\sqrt{54}}$

Write the numbers as products of primes.

$=\frac{\sqrt{3\times3\times3}\times\sqrt{2\times5\times5}}{\sqrt{2\times3\times3\times3}}$

The 2 and 3s on the top and bottom cancel out.

$=\sqrt{5\times5}$

$=5$

$\dfrac{\sqrt{27}\cdot\sqrt{50}}{\sqrt{54}}\\ =\dfrac{\sqrt{3^2\cdot 3}\cdot \sqrt{5^2\cdot 2}}{\sqrt{3^2\cdot 3\cdot 2}}\\ =\dfrac{\sqrt{3^2}\cdot \sqrt3 \cdot\sqrt{5^2}\cdot \sqrt2}{\sqrt{3^2}\cdot\sqrt{3}\cdot \sqrt{2}}\\ =\dfrac{3\cdot 5\cdot\sqrt3 \cdot \sqrt2}{3\cdot\sqrt3\cdot\sqrt2}\\ =5$