Write the cube root of 27-125-

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Cube Root Using Prime Factorisation

Write the cub...

Question

Write the cube root of $\frac{27}{125}$ .

\frac{3}{5}

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\frac{5}{3}

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\frac{4}{5}

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None of these

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Solution

The correct option is A $\frac{3}{5}$
On prime factorisation of the numbers individually, we get,
$27 = 3 \times 3 \times 3 - -------- - = 3^{3}$ .
$125 = 5 \times 5 \times 5 - -------- - = 5^{3}$ .
Therefore, cube root of $\frac{27}{125}$ is:
$\sqrt[3]{\frac{27}{125}} = \sqrt[3]{\frac{3^{3}}{5^{3}}} = \frac{3}{5}$ .

Therefore, option $A$ is correct.

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Similar questions

The expanded form of $(3 x - 5)^{3}$ is
(a) $27 x^{3} + 135 x^{2} + 225 x - 125$
(b) $27 x^{3} + 135 x^{2} - 225 x - 125$
(c) $27 x^{3} - 135 x^{2} + 225 x - 125$
(d) none of these

Q. 3, 10, 27, 4, 16, 64, 5, 25, 125

Q. Write the following numbers in the form of rational indices.
(1) Square root of 5th power of 121
(2) Cube of 4th root of 324
(3) 5th root of square of 264
(4) Cube of cube root of 3

Q. Write the opposite:

(1) +5
(2) −2
(3) −15
(4) +27
(5) 10

Solve:

[[5×{(−3)×(−4)}]÷{27 + (−14−3)}][[3×{(−4)×(−5)}]÷{27+(−13−4)}]
+[{27×(−2)}÷(−3−3)] + [{27×(−2)}÷(−3−3)]
+[{(−3)×(−3)×5}÷(−3)]]

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Write the cube root of 27125.

The correct option is A 35On prime factorisation of the numbers individually, we get,27=3×3×3––––––––––=33.125=5×5×5––––––––––=53.Therefore, cube root of 27125 is:3√27125=3√3353=35.Therefore, option A is correct.

Write the cube root of $\frac{27}{125}$ .