Mathematics: Please help with Number 25

She would have to buy 4 packages because the LCD is 60...

Please help with Number 25 - id255580432, NFMZombie

WowOK6119

21.01.2022

The product is $60-42 \sqrt{ 5}$ .

Solution:

Express the product of $3 \sqrt{20}(2 \sqrt{5}-7)$ in simplest radical form.

Given expression:

$3 \sqrt{20}(2 \sqrt{5}-7)$

To simplify the expression:

$3 \sqrt{20}(2 \sqrt{5}-7)=3 \sqrt{4\times 5}(2 \sqrt{5}-7)$

$=3 \sqrt{2^2\times 5}(2 \sqrt{5}-7)$

$=3\times 2 \sqrt{ 5}(2 \sqrt{5}-7)$

$=6 \sqrt{ 5}(2 \sqrt{5}-7)$

Multiply 6√5 into inside the bracket.

$=6 \sqrt{ 5}\times 2\sqrt{5}-6 \sqrt{ 5}\times 7$

We know that √5 × √5 = 5

$=12\times 5-42 \sqrt{ 5}$

$=60-42 \sqrt{ 5}$

$3 \sqrt{20}(2 \sqrt{5}-7)=60-42 \sqrt{ 5}$

Hence the product is $60-42 \sqrt{ 5}$ .

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