Question

Evaluate :
i) cube root of 148 Х 200​

Answer 1

Answer:

Hope it helps.............................

Answer 2

$\sqrt[3]{148 X 200}$ is 2∛3700 or, 30.9336.

Given

$\sqrt[3]{148 X 200}$

To Find

The cuberoot

Solution

$\sqrt[3]{148 X 200}$

Here we will first prime factorize 148X200

Prime Factorization of 148

148 = 2 X 2 X 37

Prime Factorization of 20

200 = 2 X 2 X 2 X 5 X 5

Therefore, the Prime Factorization of 148 X 200

= 2 X 2 X 37 X 2 X 2 X 2 X 5 X 5

Now grouping them together we get

2 X 2 X 2 X 2 X 2 X 5 X 5 X 37

For a cube root, we take 1 of the factor out for every 3 same numbers of that same factor

Hence,

$\sqrt[3]{148 X 200}$ = $2\sqrt[3]{ 2 X 2 X 5 X 5 X 37}$

Since we do not have any other triplets, our answer is

2∛3700 or, 30.9336

Hence $\sqrt[3]{148 X 200}$ is 2∛3700 or, 30.9336.

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