Question

Please help with Number 25

Answer 1

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 $60-42 \sqrt{ 5}$.