Question

please do it...guys​

Answer 1

Question

Evaluate ⇒ $\sqrt[3]{968} \times \sqrt[3]{1375}$

___________________________

Answer

We can consider this question like this → $\sqrt[3]{968\times 1375 }$

⇒ $\sqrt[3]{968\times 1375 }$

⇒ $\sqrt[3]{1331000}$

Now let's prime factorize 1331000.

$\begin{array}{c|c} \tt 2 & \sf{ 1331000} \\ \cline{1-2} \tt 2 & \sf { 665500} \\ \cline{1-2} \tt 2 & \sf{ 332750} \\ \cline{1-2} \tt 5 & \sf{ 166375} \\ \cline{1-2} \tt 5 & \sf{ 33275 }\\ \cline{1-2} \tt 5 & \sf{ 6655}\\ \cline{1-2} \tt 11 & \sf{ 1331} \\ \cline{1-2} \tt 11 & \sf{ 121 }\\ \cline{1-2} & \sf{ 11} \end{array}}$

1331000 ⇒ 2 × 2 × 2 × 5 × 5 × 5 × 11 × 11 × 11

Now we will group the prime factors with 3 same prime numbers in one group.

1331000 ⇒ (2 × 2 × 2) × (5 × 5 × 5) × (11 × 11 × 11)

We will take one number from each bracket and multiply to find the cube root.

∛1331000 ⇒ 2 × 5 × 11

∛1331000 ⇒ 10 × 11

∛1331000 ⇒ 110

∴ ∛968 × ∛1375 = 110

__________________________

Answer 2

Answer:

Refer the attachment to see the answer