QuestionApril 19, 2025

Multiply and then simplify completely: (sqrt (6)-sqrt (5))^2

Multiply and then simplify completely: (sqrt (6)-sqrt (5))^2
Multiply and then simplify completely: (sqrt (6)-sqrt (5))^2

Solution
3.8(189 votes)

Answer

1 - 2\sqrt{30} Explanation 1. Expand the expression Use the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a = \sqrt{6} and b = \sqrt{5}. 2. Calculate a^2 \sqrt{6}^2 = 6. 3. Calculate b^2 \sqrt{5}^2 = 5. 4. Calculate -2ab -2(\sqrt{6})(\sqrt{5}) = -2\sqrt{30}. 5. Combine terms Combine 6, 5, and -2\sqrt{30} to get 6 - 5 - 2\sqrt{30}.

Explanation

1. Expand the expression<br /> Use the formula $(a-b)^2 = a^2 - 2ab + b^2$. Here, $a = \sqrt{6}$ and $b = \sqrt{5}$.<br />2. Calculate $a^2$<br /> $\sqrt{6}^2 = 6$.<br />3. Calculate $b^2$<br /> $\sqrt{5}^2 = 5$.<br />4. Calculate $-2ab$<br /> $-2(\sqrt{6})(\sqrt{5}) = -2\sqrt{30}$.<br />5. Combine terms<br /> Combine $6$, $5$, and $-2\sqrt{30}$ to get $6 - 5 - 2\sqrt{30}$.
Click to rate:

Similar Questions