Question

Æ Rationalize 4 /√16​

Answer 1

Rationalization

We are asked to rationalize the following expression:

$\implies \dfrac{4}{\sqrt{16}}$

In-order to rationalize the given expression, we need to rationalize the fractions been operated on as their denominators are irrational. And in order to rationalize the denominator, we multiply the denominator's rationalising factor with the numerator and the denominator of the fraction so that it's denominator becomes rational.

Now, just multiply √16 with both the numerator and the denominator to rationalise the denominator.

$\implies \dfrac{4}{\sqrt{16}} \times \dfrac{\sqrt{16}}{\sqrt{16}}$

Rearrange the terms in order to perform multiplication.

$\implies \dfrac{4(\sqrt{16})}{\sqrt{16}(\sqrt{16})}$

Organize the part that can be taken out of the radical sign inside the square root symbol.

$\implies \dfrac{4(4)}{\sqrt{16}(\sqrt{16})}$

Simplify the denominator term by using the identity √a × √a = a. Here √16 is there in the place of √a, so √16 × √16 = 16.

$\implies \dfrac{4(4)}{16}$

Perform multiplication in the numerator.

$\implies \dfrac{16}{16}$

The last step, cancel the required fraction.

$\implies \boxed{1}$

Hence, rationalized.

Answer 2

Given:-

• $\sf \: \frac{4}{ \sqrt{16} }$

To Find:-

• Rationalize

Solution:-

$= \boxed{ \red{ \bf \frac{4}{ \sqrt{16} } \times \frac{ \sqrt{16} }{ \sqrt{16} } }} \\ = \boxed{ \green{ \bf\frac{4}{ \sqrt{16} } \times \frac{4}{ \sqrt{16} } }} \\ = \boxed{ \pink{ \bf \frac{4 \times 4}{ \sqrt{16 \times } \sqrt{16} }} } \\ = \bf \boxed{ \blue {\bf\frac{16}{16 } = 1\: \: \: \: \: \: \: \: \: } }$