Question

the value of cube ³√ 700×2×49×5​

Answer 1

Answer:

70

Step-by-step explanation:

∛700 × 2 × 49 × 5

= ∛(1400 × 245)

= ∛343000

Now do prime factorisation of 343000

(refer attachment for prime factorisation)

So, the Factors of 343000

= 2 × 2 × 2 × 5 × 5 × 5 × 7 × 7 × 7

= 2³ × 5³ × 7³

= (2 × 5 × 7)³

= (70)³

This can be written as:

343000 = (70)³

Taking cube root on both sides,

∛(343000) = ∛(70)³

→ ∛(343000) = 70

∴ ∛(343000) = 70

REMEMBER:

• While taking the cube root of a real number, after doing its prime factorisation, group it in triplets (3 same numbers in 1 group)

• While taking square root of a real number, group it in pairs