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

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

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Answer 1 · 2017-05-04T22:03:15

See a solution process below:

Explanation:

This is a special form of the quadratic factored:

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

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

$(\sqrt{2} + \sqrt{7}) (\sqrt{2} + \sqrt{7}) = {\sqrt{2}}^{2} + 2 \sqrt{2} \sqrt{7} + {\sqrt{7}}^{2} =$ $(sqrt(2) + sqrt(7))(sqrt(2) + sqrt(7)) = sqrt(2)^2 + 2sqrt(2)sqrt(7) + sqrt(7)^2 =$

$2 + 2 \sqrt{2} \sqrt{7} + 7$ $2 + 2sqrt(2)sqrt(7) + 7$

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

$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ $sqrt(a) * sqrt(b) = sqrt(a * b)$

$2 + 2 \sqrt{2 \cdot 7} + 7 =$ $2 + 2sqrt(2 * 7) + 7 =$ 2 + 2sqrt(14) + 7 =#

$9 + 2 \sqrt{14}$ $9 + 2sqrt(14)$

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

1 Answer

Explanation:

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

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