Question

Tiles

4V3
332
233
375
Pairs
324
1
V48
1 1 1
354
745

Answer 1

Given:

The expressions are:

`\sqrt[3]{24},√(48),\sqrt[3]{54},√(45)`

To find:

The simplified form of each expression.

Solution:

We have,

`\sqrt[3]{24}`

It can be written as:

`\sqrt[3]{24}=\sqrt[3]{2* 2* 2* 3}`

`\sqrt[3]{24}=2\sqrt[3]{3}`

Similarly,

`√(48)=√(2* 2* 2* 2* 3)`

`√(48)=(2* 2)√(3)`

`√(48)=4√(3)`

And,

`\sqrt[3]{54}=\sqrt[3]{2* 3* 3* 3}`

`\sqrt[3]{54}=3\sqrt[3]{2}`

In the same way,

`√(45)=√(3* 3* 5)`

`√(45)=3√(5)`

Therefore, the required pairs are:

`\sqrt[3]{24}\to 2\sqrt[3]{3}`

`√(48)\to 4√(3)`

`\sqrt[3]{54}\to 3\sqrt[3]{2}`

`√(45)\to 3√(5)`