Question

Cube root of 3 and square root of 2 which is the biggest

Answer 1

In cube root of 3 and square root of 2, the value of the root is 3 and 2 respectively. So, the L.C.M is 6.

Now, when the cube root of 3's cube root is multiplied by two it becomes the 6th root. Three from cube root of 3 becomes 3^2 i.e 9.

Similarly, square root of 2's square root is multiplied by 3 to get sixth root. Two from square root of 2 becomes 2^3 i.e 8.

Thus cube root of 3 can be written as sixth root of 9 and square root of 2 as sixth root of 8.

From this, we conclude that cube root of 3 is greater than square root of 2 as sixth root of 9 is greater than sixth root of 8.

Answer 2

Answer: Cube root of 3= $\sqrt[3]{3}$and

square root of 2  =$\sqrt{2}$

$\sqrt[3]{3}$ is bigger than $\sqrt{2}$

Step-by-step explanation:

$\sqrt[3]{3}$ =3^1/3

$\sqrt{2}$=2^1/2

L.C.M OF 3,2 IS 6

Now,Three from cube root of 3 becomes 3^2 i.e 9.

3^1/3= 3^2/6 and

3^1/3= 9^1/6 and

Similarly, Two from square root of 2 becomes 2^3 i.e 8.

2^1/2 = 2^3/6

2^1/2 = 8^1/6

here 9^1/6 greater than 8^1/6

⇒     3^1/3 greater than 2^1/2