Write the simplest form of rationalising factor for the given surd.i.�

1.	Write the simplest form of rationalising factor for the given surd.i. \(\frac{3}{5}\sqrt{10}\) 3/5√10ii. \(3\sqrt{72}\) 3√72iii. \(4\sqrt{11}\) 4√11
Answer» 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 \(4\sqrt{11}\).

Write the simplest form of rationalising factor for the given surd.i. \(\frac{3}{5}\sqrt{10}\) 3/5√10ii. \(3\sqrt{72}\) 3√72iii. \(4\sqrt{11}\) 4√11

Answer»

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 \(4\sqrt{11}\).