جواب کار در کلاس صفحه 75 درس 4 ریاضی نهم (توان و ریشه)

1

\(\begin{array}{l}\sqrt {98} - \sqrt {50} + \sqrt {128} = \\\\\sqrt {{7^2} \times 2} - \sqrt {{5^2} \times 2} + \sqrt {{8^2} \times 2} = \\\\7\sqrt 2 - 5\sqrt 2 + 8\sqrt 2 = 10\sqrt 2 \end{array}\)

2

\(\begin{array}{l}\sqrt {27} - \sqrt {12} - \sqrt {75} + \sqrt {48} = \\\\\sqrt {{3^2} \times 3} - \sqrt {{2^2} \times 3} - \sqrt {{5^2} \times 3} + \sqrt {{2^4} \times 3} = \\\\3\sqrt 3 - 2\sqrt 3 - 5\sqrt 3 + 4\sqrt 3 = 0\end{array}\)

3

\(\begin{array}{l}5\sqrt[3]{2} \times 3\sqrt[3]{{54}} - 4\sqrt[3]{{128}} = \\\\5\sqrt[3]{2} + 3\sqrt[3]{{{3^2} \times 2}} - 4\sqrt[3]{{{2^6} \times 2}} = \\\\5\sqrt[3]{2} + 3 \times 3\sqrt[3]{2} - 4\sqrt[3]{{{2^3} \times {2^3} \times 2}} = \\\\5\sqrt[3]{2} + 9\sqrt[3]{2} - 4 \times 2 \times 2\sqrt[3]{2} = \\\\14\sqrt[3]{2} - 16\sqrt[3]{2} = - 2\sqrt[3]{2}\end{array}\)

4

\(\begin{array}{l}\sqrt {4 + \frac{1}{{81}} + \frac{4}{9}} = \\\\\sqrt {\frac{{324 + 1 + 36}}{{81}}} = \\\\\sqrt {\frac{{361}}{{81}}} = \frac{{19}}{9}\end{array}\)

5

\(\begin{array}{l}\left( {\sqrt 2 + \sqrt 3 } \right)\left( {3\sqrt 2 - \sqrt 3 } \right) = \\\\3\sqrt 2 \times \sqrt 2 - \sqrt 2 \times \sqrt 3 + 3\sqrt 2 \times \sqrt 3 - \sqrt 3 \times \sqrt 3 = \\\\3\sqrt {{2^2}} - \sqrt 6 + 3\sqrt 6 - \sqrt {{3^2}} = 6 - \sqrt 6 + 3\sqrt 6 - 3 = \\\\ = 3 + 2\sqrt 6 \end{array}\)