The product is [tex]60-42 \sqrt{ 5}[/tex].
Solution:
Express the product of [tex]3 \sqrt{20}(2 \sqrt{5}-7)[/tex] in simplest radical form.
Given expression:
[tex]3 \sqrt{20}(2 \sqrt{5}-7)[/tex]
To simplify the expression:
[tex]3 \sqrt{20}(2 \sqrt{5}-7)=3 \sqrt{4\times 5}(2 \sqrt{5}-7)[/tex]
[tex]=3 \sqrt{2^2\times 5}(2 \sqrt{5}-7)[/tex]
[tex]=3\times 2 \sqrt{ 5}(2 \sqrt{5}-7)[/tex]
[tex]=6 \sqrt{ 5}(2 \sqrt{5}-7)[/tex]
Multiply 6√5 into inside the bracket.
[tex]=6 \sqrt{ 5}\times 2\sqrt{5}-6 \sqrt{ 5}\times 7[/tex]
We know that √5 × √5 = 5
[tex]=12\times 5-42 \sqrt{ 5}[/tex]
[tex]=60-42 \sqrt{ 5}[/tex]
[tex]3 \sqrt{20}(2 \sqrt{5}-7)=60-42 \sqrt{ 5}[/tex]
Hence the product is [tex]60-42 \sqrt{ 5}[/tex].
