i. \(\frac{3}{5}\sqrt{10}\)
3/5√10
= \(\frac{3}{5}\sqrt{10}\) x \(\sqrt{10}\)
= \(\frac{3}{5}\times10\)
= 3 x 2
= 6, which is a rational number.
∴ √10 is the simplest form of the rationalising factor of \(\frac{3}{5}\sqrt{10}\) .
ii. \(3\sqrt{72}\)
3√72
= \(3\sqrt{36\times2}\) =3 x \(6\sqrt{2}\) = \(18\sqrt{2}\)
Now, 18√2 x √2 = 18 x 2 = 36, which is a rational number.
∴ √2 is the simplest form of the rationalising factor of \(3\sqrt{72}\)
iii. \(4\sqrt{11}\)
4√11
\(4\sqrt{11}\) x \(\sqrt{11}\) = 4 x 11 =44 which is a rational number.
∴ √11 is the simplest form of the rationalising factor of \(4\sqrt{11}\).
