Question

what is the rationalising factor of 2^3√5​

Answer 1

Given

2(<superscript> 3 </superscript> √5)

Prime factorization of 125 = 5 × 5 × 5

So, <superscript> 3 </superscript> √125 = <superscript> 3√5 </superscript> × 5 × 5 = 5

Now, 2(<superscript> 3 </superscript> √5) × <superscript> 3 </superscript> √25 = (<superscript> 3 </superscript> √5 × 25) =2( 3√125) = 10

Thus, when2(<superscript> 3 </superscript> √5) is multiplied by 3√25, we obtain the rational number 10

Therefore, the rationalizing factor of 2(<superscript> 3 </superscript> √5) is <superscript> 3 </superscript> √25