Question

$\sqrt{ \sqrt{ \frac{64}{25} \times \sqrt{ \frac{144}{25} } } }$
please write the correct answer step by step ​

Answer 1

Answer:

Solve the roots

ROOT(8/5 ×12/5)

Answer 2

Answer:

Step-by-step explanation:

ANSWER:-

We will do this via simplification.

• In simplification, we will first solve the inner square roots.
• Then we will apply properties( Associative, distributive etc)

Let's solve!

$\sqrt{\sqrt{\dfrac{64}{25} \times \dfrac{144}{25}}}$

$\sqrt{\sqrt{(\dfrac{8}{5})^{2} \times (\dfrac{12}{5})^{2}}}$

$\sqrt{\sqrt{(\dfrac{8 \times 12}{5 \times 5})^2}}$

Now, as I have taken the whole in power 2, it cancels the inner square root.

Now, we have leftover as:-

$\sqrt{\dfrac{8 \times 12}{5 \times 5}}$

$\sqrt{\dfrac{96}{25}}$

Now, as 96 is not any square root, so we will leave as it is.

And we will replace 25 by 5.

$\dfrac{\sqrt{96}}{5}$ is the answer.