Question

The simplest rationalisation factor of 500 is?
plzz tell the correct answer with correct explanation ​

Answer 1

Answer:

The rationalizing factor of \sqrt[3]{500}

3

500

is 2^{\frac{1}{3}}2

3

1

Step-by-step explanation:

Given : Number \sqrt[3]{500}

3

500

To find : The simplest rationalizing factor of the given number?

Solution :

First we find the cube root of the number 500,

\sqrt[3]{500}

3

500

=(500)^{\frac{1}{3}}=(500)

3

1

=(5^3\times 2^2)^{\frac{1}{3}}=(5

3

×2

2

)

3

1

=(5^{\frac{3}{3}}\times 2^{\frac{2}{3}})=(5

3

3

×2

3

2

)

=(5\times 2^{\frac{2}{3}})=(5×2

3

2

)

So, The rationalizing factor of \sqrt[3]{500}

3

500

is 2^{\frac{1}{3}}2

3

1

As =(500)^{\frac{1}{3}}\times 2^{\frac{1}{3}}=(500)

3

1

×2

3

1

=(5\times 2^{\frac{2}{3}})\times 2^{\frac{1}{3}}=(5×2

3

2

)×2

3

1

=5\times 2^{\frac{2}{3}+\frac{1}{3}}=5×2

3

2

+

3

1

=5\times 2^{1}=5×2

1

=5\times 2=5×2

=10=10

10 is a rational number.

Therefore, The rationalizing factor of \sqrt[3]{500}

3

500

is 2^{\frac{1}{3}}2

3

1