Pergunta

Express the product (sqrt (10)-sqrt (7))(sqrt (10)+sqrt (7)) in simplest form. Answer Attempt 2ont of 3
Solução

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JoãoMestre · Tutor por 5 anos
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To simplify the expression $(\sqrt {10}-\sqrt {7})(\sqrt {10}+\sqrt {7})$, we can use the difference of squares formula, which states that $(a - b)(a + b) = a^2 - b^2$.<br /><br />In this case, $a = \sqrt{10}$ and $b = \sqrt{7}$. Applying the formula, we get:<br /><br />$(\sqrt{10} - \sqrt{7})(\sqrt{10} + \sqrt{7}) = (\sqrt{10})^2 - (\sqrt{7})^2$<br /><br />Simplifying further, we have:<br /><br />$(\sqrt{10})^2 = 10$<br /><br />$(\sqrt{7})^2 = 7$<br /><br />Therefore, the expression simplifies to:<br /><br />$10 - 7 = 3$<br /><br />So, the simplified form of the expression $(\sqrt {10}-\sqrt {7})(\sqrt {10}+\sqrt {7})$ is $\boxed{3}$.
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