Question

Simplify 2/3 root 144/64 and state whether the result is rational or irrational number

(no copied answer)​

Answer 1

Solution!!

We have to simplify $\sf \dfrac{2}{3}\sqrt{\dfrac{144}{64}}$. The result will be either rational or irrational number so, let's find out.

$\sf \dfrac{2}{3}\sqrt{\dfrac{144}{64}}$

The fraction under in the square root can be reduced with 16. It will make it simpler to calculate the answer.

= $\sf \dfrac{2}{3}\sqrt{\dfrac{9}{4}}$

Now, let's calculate the square root.

= $\sf \dfrac{2}{3}\sqrt{\dfrac{3\times 3}{2\times 2}}$

= $\sf \dfrac{2}{3}\times \dfrac{3}{2}$

Reduce the numbers with greatest common factor 2 and 3.

= $\sf 1$

Hence, $\dfrac{2}{3}\sqrt{\dfrac{144}{64}}$ equals 1, which is a rational number.