Question

How do you simplify \[{\left( {125} \right)^{\dfrac{1}{3}}}\]?

Answer 1

Hint:In order to write the expression into the simplest form, factorize the base part of the value inside the bracket as\[{5^3}\] and the property of exponents that${({a^m})^n} = {a^{m \times n}}$to find the desired answer.


Formula Used:
${(a)^{\dfrac{m}{n}}}$=${({a^m})^{\dfrac{1}{n}}}$
${x^{m + n}} = {x^m} \times {x^n}$

Complete step by step solution:
Given a number
\[{\left( {125} \right)^{\dfrac{1}{3}}}\]

Separating the value $125$ into its factors, So the factors of $125$ comes to be,
$1,5,25,125$

Now let’s find the factors who are perfect cubes
$1,5$

From the above we can say that $125 = 5 \times 5 \times 5$
Replace $125$as $5 \times 5 \times 5$ in the original number

\[
= {\left( {5 \times 5 \times 5} \right)^{\dfrac{1}{3}}} \\
= {({5^3})^{\dfrac{1}{3}}} \\
\]

Using proper of exponents ${({a^m})^n} = {a^{m \times n}}$
\[
= {5^{3 \times \dfrac{1}{3}}} \\
= 5 \\
\]

Therefore, \[{\left( {125} \right)^{\dfrac{1}{3}}}\]in the simplest form is equal to $5$.

Additional Information: 1. To calculate fraction from the percentage, divide the given percentage value by 100

For example: We have to write $70\% $into fraction
$

= \dfrac{{70}}{{100}} \\
= \dfrac{7}{{10}} \\
$
Or
$ = 0.7$

2. If you want to Increase a Number by y %:
Example: On the off chance that a number is expanded by\[10{\text{ }}\% \], at that point it becomes 1.1 times of itself.

On the off chance that a number is expanded by 30 %, at that point it becomes 1.3 times of itself.

3. If you want to Decrease a Number by y %:
Example: On the off chance that a number is diminished by 10 %, at that point it becomes 0.90 times of itself.

On the off chance that a number is diminished by 30 %, at that point it becomes 0.70 times of itself.

Note: 1. Don’t Forgot to cross check the answer.
2.Factorise the number inside the square root properly to get knowledge of every perfect square