How do you simplify 2 cubed root 81 + 3 cubed root 24?

Question

How do you simplify 2 cubed root 81 + 3 cubed root 24?

2 Answers

Impact of this question

5456 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-15T14:44:09

The answer is $12 \sqrt[3]{3}$ $12root(3)3$ and the solution follows.

Explanation:

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 (24 is 3 x 8, and 8 is a perfect cube, and 81 is 3 x 27; 27 is a perfect cube).

This allows you to simplify the problem as shown here:

$2 \sqrt[3]{81} + 3 \sqrt[3]{24}$ $2root(3)81+3root(3)24$

$2 \sqrt[3]{27 \times 3} + 3 \sqrt[3]{8 \times 3}$ $2root(3)(27xx3)+3root(3)(8xx3)$

$2 (\sqrt[3]{27} \times \sqrt[3]{3}) + 3 (\sqrt[3]{8} \times \sqrt[3]{3})$ $2(root(3)(27)xxroot(3)(3))+3(root(3)(8)xxroot(3)(3))$

This step is true because $\sqrt[3]{a \times b} = \sqrt[3]{a} \times \sqrt[3]{b}$ $root(3)(axxb) = root(3)axxroot(3)b$
I've put in some brackets in the hope of keeping this clear.

$2 (3 \times \sqrt[3]{3}) + 3 (2 \times \sqrt[3]{3})$ $2(3xxroot(3)(3))+3(2xxroot(3)(3))$

$6 \sqrt[3]{3} + 6 \sqrt[3]{3} = 12 \sqrt[3]{3}$ $6root(3)(3)+6root(3)(3) = 12root(3)3$

Answer 2 · 2018-03-15T14:49:17

$12 \sqrt[3]{3}$ $12root(3)3$

Explanation:

$2 \sqrt[3]{81} + 3 \sqrt[3]{24} = 2 \sqrt[3]{27.3} + 3 \sqrt[3]{8.3}$ $2root(3)81+3root(3)24 =2root(3)27.3+3root(3)8.3$

$= 2.3 \sqrt[3]{3} + 3.2 \sqrt[3]{3} = 6 \sqrt[3]{3} + 6 \sqrt[3]{3} = 12 \sqrt[3]{3}$ $=2.3root(3)3+3.2root(3)3= 6root(3)3+6root(3)3 = 12root(3)3$

Science

Math

Humanities

... and beyond

How do you simplify 2 cubed root 81 + 3 cubed root 24?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question