How do you simplify $(sqrt2+sqrt7)(sqrt 2+sqrt 7)$ ?

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Answer 1 · 2017-05-04T22:03:15

See a solution process below:

This is a special form of the quadratic factored:

$(a + b)^2 = (a + b)(a + b) = a^2 + 2ab + b^2$

Substituting $sqrt(2)$ for $a$ and $sqrt(7)$ for $b$ gives:

$(sqrt(2) + sqrt(7))(sqrt(2) + sqrt(7)) = sqrt(2)^2 + 2sqrt(2)sqrt(7) + sqrt(7)^2 =$

$2 + 2sqrt(2)sqrt(7) + 7$

We can now use this rule for multiplying radicals to simplify the middle term:

$sqrt(a) * sqrt(b) = sqrt(a * b)$

$2 + 2sqrt(2 * 7) + 7 =$ 2 + 2sqrt(14) + 7 =#

$9 + 2sqrt(14)$

How do you simplify (sqrt2+sqrt7)(sqrt 2+sqrt 7)(sqrt2+sqrt7)(sqrt 2+sqrt 7)?