Question

4) Simplify:
3√128
250​

Answer 1

Step-by-step explanation:

1152. 250

$1152 > 250$

Answer 2

SOLUTION

TO SIMPLIFY

$\displaystyle \sf{ \sqrt[3]{ \frac{128}{250} } }$

EVALUATION

Here the given expression is

$\displaystyle \sf{ \sqrt[3]{ \frac{128}{250} } }$

Now

$\displaystyle \sf{\frac{128}{250} }$

$\displaystyle \sf{ = \frac{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}{2 \times 5 \times 5 \times 5} }$

$\displaystyle \sf{ = \frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{5 \times 5 \times 5} }$

$\displaystyle \sf{ = \frac{ {2}^{3} \times {2}^{3} }{ {5}^{3} } }$

Now we have

$\displaystyle \sf{ \sqrt[3]{ \frac{128}{250} } }$

$\displaystyle \sf{ = \sqrt[3]{ \frac{ {2}^{3} \times {2}^{3} }{ {5}^{3} } } }$

$\displaystyle \sf{ = \frac{2 \times 2}{5} }$

$\displaystyle \bf{ = \frac{4}{5} }$

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