Answer

Verified

417.6k+ views

**Hint:**Here, we are asked to solve $2\sqrt[3]{{81}} + 3\sqrt[3]{{24}}$ To solve this , we first need to look at the values whose cube roots are involved in the problem and determine whether they are perfect cubes or whether they contain factors which are perfect cubes. Then we will find the cube roots of these perfect cubes and simplify the expression.

**Complete step-by-step solution:**

We need to simplify the term $2\sqrt[3]{{81}} + 3\sqrt[3]{{24}}$. We will first consider the two numbers given in the cube root and convert them as the product of numbers one of which will be the perfect cube. The first number is 81. This number can be written as a product of two numbers 3 and 27. We know that 27 is the perfect cube, so we can easily find its cube root.

We can write

$81 = 3 \times 27 = 3 \times 3 \times 3 \times 3 = 3 \times {3^3}$

The second number is 24. This number can be written as a product of two numbers 3 and 8. We know that 8 is the perfect cube, so we can easily find its cube root.

We can write

$24 = 3 \times 8 = 3 \times 2 \times 2 \times 2 = 3 \times {2^3}$

Now, we will simplify the given expression.

$

2\sqrt[3]{{81}} + 3\sqrt[3]{{24}} \\

= 2\sqrt[3]{{3 \times {3^3}}} + 3\sqrt[3]{{3 \times {2^3}}} \\

$

We know that $\sqrt[3]{{{a^3}}} = a$

Therefore,

$

2\sqrt[3]{{81}} + 3\sqrt[3]{{24}} \\

= 2\sqrt[3]{{3 \times {3^3}}} + 3\sqrt[3]{{3 \times {2^3}}} \\

= 2 \times 3\sqrt[3]{3} + 3 \times 2\sqrt[3]{3} \\

= 6\sqrt[3]{3} + 6\sqrt[3]{3} \\

= 12\sqrt[3]{3} \\

$

Thus, our final answer is $12\sqrt[3]{3}$.

**Note:**Here, we have determined the cube roots while solving this question. To find the cubic root of a number easily, we can use the prime factorization method. By evaluating the prime factors we can pair similar digits in a group of three and take them out as a single digit from the cubic root.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

How do you graph the function fx 4x class 9 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The only snake that builds a nest is a Krait b King class 11 biology CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Why is there a time difference of about 5 hours between class 10 social science CBSE

Which places in India experience sunrise first and class 9 social science CBSE