Question

the simplest rationalising factor of 3√500

Answer 1

Answer:

The rationalizing factor of $\sqrt[3]{500}$  is $2^{\frac{1}{3}}$

Step-by-step explanation:

Given : Number $\sqrt[3]{500}$

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

Solution :  

First we find the cube root of the number 500,

$\sqrt[3]{500}$

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

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

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

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

So, The rationalizing factor of $\sqrt[3]{500}$  is $2^{\frac{1}{3}}$

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

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

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

$=5\times 2^{1}$

$=5\times 2$

$=10$

10 is a rational number.

Therefore, The rationalizing factor of $\sqrt[3]{500}$  is $2^{\frac{1}{3}}$

Answer 2

Answer:

$Rationalising \: factor \: of \: \sqrt[3]{500}\\=5\times 2^{\frac{2}{3}} \: is 2^{\frac{1}{3}}$

Step-by-step explanation:

$Write \: the \: least \: form \: given \: number\\ \sqrt[3]{500}\\=\sqrt[3]{(5\times 5\times 5)\times 2 \times2}\\=5\sqrt[3]{2^{2}}\\=5\times 2^{\frac{2}{3}}$

$Rationalising \: factor \: of \: \sqrt[3]{500}\\=5\times 2^{\frac{2}{3}} \: is 2^{\frac{1}{3}}$

$Product\: of \: 5\times 2^{\frac{2}{3}} \times 2^{\frac{1}{3}} = 5\times 2^{\frac{2}{3}+\frac{1}{3}}\\=5\times 2^{\frac{2+1}{3}}\\=5\times 2^{\frac{3}{3}}\\=5\times 2\\=10 \: (Rational \: number )$

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