What is $(1-3sqrt7)(4-3sqrt7)$ ?

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Answer 1 · 2016-03-16T11:53:11

$(1-3sqrt(7))(4-3sqrt(7))=67-15sqrt(7)$

You could think that

$sqrt(7)=a$

Therefore

$(1-3sqrt(7))(4-3sqrt(7))=(1-3a)(4-3a)$

that becomes a polinomial product

$(1-3a)(4-3a)=1*4-1*3a-3a*4+(3a)^2=$
$=4-3a-12a+9a^2=4-15a+9a^2=$

Now you substitute $a$ with $sqrt(7)$

$=4-15sqrt(7)+9*7=4+63-15sqrt(7)=67-15sqrt(7)$

With practice you will be able to avoid the substitution and compute the product immediately.

What is (1-3sqrt7)(4-3sqrt7)(1-3sqrt7)(4-3sqrt7)?