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Mathematics

Grade-8

Easy

Question

Which of the following is the cube root of $fraction numerator negative 64 over denominator 343 end fraction$ ?

$\frac{7}{4}$
$\frac{- 7}{4}$
$\frac{4}{7}$
$\frac{- 4}{7}$

hint Hint:

We will use prime factorization on the given number and then simplify the same to find the solution.

The correct answer is: $fraction numerator negative 4 over denominator 7 end fraction$

GIVEN-
Given number = -64/343
TO FIND-
Cube root of the given number.
SOLUTION-
Using prime factorization, we know that-
– 64 = – 4 x – 4 x – 4
343 = 7 x 7 x 7
∴ ³√(-64/343) = ³√(-4 * -4 * -4)/(7 * 7 * 7)
∴ ³√(-64/343) = ³√(-4 * -4 * -4) / ³√(7 * 7 * 7)
∴ ³√(-64/343) = -4 / 7
FINAL ANSWER-
Option 'b' i.e. '-4/7' is the correct answer to the given question.

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