Question

Evaluate : ³√1372× ³√1458

Answer 1

First we have to find the cube root of 1372 and 1458 by the prime factorisation method. Then we will get;
 
 ∛1372 =  ∛2×2×7×7×7 (after factorizing)
    i.e; ∛1372 = 7√4

∛1458 = ∛2×3×3×3×3×3×3
∛1458 =  3×3√2 = 9√2

so ∛1372 × ∛1458 = 7√4 × 9√2 = 63√8 (we can simplify √8 = 2√2)
                                               So the final answer = 63×2√2
                                                                              =  126√2
 
Hope this is right................... 

 

Answer 2

"$\sqrt[3]{1372} \times \sqrt[3]{1458}=126 \sqrt{2}$

Given:

$\sqrt[3]{1372} \times \sqrt[3]{1458}$

Solution:

First we should find the cube root of 1372 and 1458 by the prime factorisation method:

$\sqrt[3]{1372}=2 \times 2 \times 7 \times 7 \times 7 (After factorizing)$

$\Rightarrow \sqrt[3]{1372}=7 \sqrt{4}$

$\sqrt[3]{1458}=2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 (After factorizing)$

$\sqrt[3]{1458}=\sqrt{2} \times 3 \times 3=9 \sqrt{2}$

So,

$\sqrt[3]{1372} \times \sqrt[3]{1458}=7 \sqrt{4} \times 9 \sqrt{2}=63 \sqrt{8}(\because \sqrt{8}=2 \sqrt{2})$

$=63 \times 2 \sqrt{2}$

$\sqrt[3]{1372} \times \sqrt[3]{1458}=126 \sqrt{2}"$