Evaluate- -8- 17- 17- 17-

On prime factorising, we get, 8=2 × 2× 2 .Then, √(8× 17× 17× 17) =√(2× #160;2× 2×17× 17× 17) =2× 17 =34 .Therefore, 34 is the sol ...

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Standard VIII

Mathematics

Finding Square Root through Prime Factorisation

Evaluate: √...

Question

Evaluate: $\sqrt[3]{8 \times 17 \times 17 \times 17}$ .

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Solution

On prime factorising, we get,
$8 = 2 \times 2 \times 2 - -------- -$ .
Then,
$\sqrt[3]{8 \times 17 \times 17 \times 17}$
$= \sqrt[3]{2 \times 2 \times 2 - -------- - \times 17 \times 17 \times 17 - ------------ -}$
$= 2 \times 17$
$= 34$ .

Therefore, $34$ is the solution.

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Evaluate: 3√8×17×17×17.

On prime factorising, we get,8=2×2×2––––––––––.Then,3√8×17×17×17=3√2×2×2––––––––––×17×17×17––––––––––––––=2×17=34.Therefore, 34 is the solution.

Evaluate: $\sqrt[3]{8 \times 17 \times 17 \times 17}$ .

On prime factorising, we get,
$8 = 2 \times 2 \times 2 - -------- -$ .
Then,
$\sqrt[3]{8 \times 17 \times 17 \times 17}$
$= \sqrt[3]{2 \times 2 \times 2 - -------- - \times 17 \times 17 \times 17 - ------------ -}$
$= 2 \times 17$
$= 34$ .

Therefore, $34$ is the solution.