Question

How do you find the cube root of \[0.000343\] ?

Answer 1

Hint: In this question, we need to find the cube root of \[0.000343\] . In order to find the cube root of the given decimal number, first we need to write the decimal number as a fraction with numerator and denominator. Then we can find the cube root of the numerator and denominator using the factorization method. After getting the cube root of the numerator and denominator using the factorization method, we can again write the fraction as a decimal number.

Complete step-by-step answer:
Given, \[0.000343\]
Here we need to find the cube root of a given decimal number.
We need to express the given decimal number as a fraction.
We can write \[0.000343\] as \[\dfrac{343}{1000000}\]
Now we can find the cube root of the numerator and denominator using the factorization method. Since both the numerator and the denominator are perfect cube numbers.
First, we can write the numerator as the product of the factors,
\[343 = 7 \times 7 \times 7\]
Now we can write the denominator as the product of the factors,
\[1000000 = 10 \times 10 \times 10 \times 10 \times 10 \times 10\]
We can see that \[7\] occurs three times in the numerator and \[10\] occurs six times in the denominator.
Now we can find the cube root of \[0.000343\]
\[\sqrt[3]{\left( 0.000343 \right)} = \sqrt[3]{\left( \dfrac{343}{1000000} \right)}\]
By substituting, the factors of numerator and denominator,
We get,
\[\Rightarrow \sqrt[3]{\dfrac{7 \times 7 \times 7}{10 \times 10 \times 10 \times 10 \times 10 \times 10}}\ \]
On taking terms out of cubical sign,
We get,
\[\Rightarrow \dfrac{7}{10 \times 10}\]
On simplifying,
We get,
\[\Rightarrow \dfrac{7}{100}\]
Now, we need to again write this fraction in the form of decimals.
On further simplifying,
We get,
\[\Rightarrow \ 0.07\]
Thus the cube root of \[0.000343\] is \[0.07\]
Final answer :
The cube root of \[0.000343\] is \[0.07\] .

Note: The number given in the question is a decimal number. A decimal number is nothing but a number whose decimal part and the whole number part is separated by a decimal point. A decimal number can be converted into fraction and then again can be converted into decimal form. We should be very careful in factorising the given number and we can cross-check it, if they are getting the same number by multiplication of factors or not.