Question

Evaluate cube root of 0.027 upon 0.008 / square root of 0.09 upon 0.04 -1

Answer 1

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Answer 2

Answer:

The required answer is $3$.

Step-by-step explanation:

Concept:

The factor we multiply by itself three times to obtain a number is its cube root. $3$ cube root of, end cubic root is the symbol for the cube root. The opposite of cubing an integer is to get its cube root.

Given:

It is provided that $\frac{\sqrt[3]{\frac{0.0127}{0.0008}}}{{\sqrt[]{\frac{0.09}{0.04}-1}}}$

To find:

We have to evaluate $\frac{\sqrt[3]{\frac{0.0127}{0.0008}}}{{\sqrt[]{\frac{0.09}{0.04}-1}}}$.

Solution:

We have,

$\frac{\sqrt[3]{\frac{0.0127}{0.0008}}}{{\sqrt[]{\frac{0.09}{0.04}-1}}}$

Firstly we have to resolve all the provided terms,

$&\mathbf{0 . 0 2 7}=27 / 1000=(3 \times 3 \times 3) /(10 \times 10 \times 10)=3^{3} / 10^{3}=(3 / 10)^{3}=(0.3)^{3}$

$&\mathbf{0 . 0 0 8}=8 / 1000=(2 \times 2 \times 2) /(10 \times 10 \times 10)=2^{3} / 10^{3}=(2 / 10)^{3}=(0.2)^{3}$

$&\mathbf{0 . 0 9}=9 / 100=(3 \times 3) /(10 \times 10)=(3 / 10)^{2}=(0.3)^{2}$

$&0.04=4 / 100=(2 \times 2) /(10 \times 10)=(2 / 10)^{2}$$&=(0.2)^{2}$

Now,

$\sqrt[3]{\frac{0.027}{0.08}}=\sqrt[3]{\frac{(0.3)^{3}}{(0.2)^{3}}}$

$&\frac{0.3}{0.2}=1.5$

$\sqrt{\frac{0.09}{0.04}}=\sqrt{\frac{(0.3)^{2}}{(0.2)^{2}}}$

$&\frac{0.3}{0.2}=1.5$

Thus,

$\frac{\sqrt[3]{\frac{0.0127}{0.0008}}}{{\sqrt[]{\frac{0.09}{0.04}-1}}}$

$=$ $\frac{1.5}{(1.5)-1}$

$=\frac{1.5}{(0.5)}$

$&=3$

The required answer is $3$.

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