Bài 3: Liên hệ giữa phép nhân và phép khai phương
Hướng dẫn giải Bài 22 (Trang 15 SGK Toán 9, Tập 1)
<p><strong>B&agrave;i 22 (Trang 15 SGK To&aacute;n 9, Tập 1):</strong></p> <p>Biến đổi dạng thức dưới dấu căn th&agrave;nh dạng t&iacute;ch rồi t&iacute;nh:</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo>&#160;</mo><msqrt><msup><mn>13</mn><mn>2</mn></msup><mo>-</mo><msup><mn>12</mn><mn>2</mn></msup></msqrt><mo>;</mo><mspace linebreak="newline"/><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo>)</mo><mo>&#160;</mo><msqrt><msup><mn>17</mn><mn>2</mn></msup><mo>-</mo><mn>8</mn></msqrt><mo>;</mo><mspace linebreak="newline"/><mspace linebreak="newline"/><mi mathvariant="normal">c</mi><mo>)</mo><mo>&#160;</mo><msqrt><msup><mn>117</mn><mn>2</mn></msup><mo>-</mo><msup><mn>108</mn><mn>2</mn></msup></msqrt><mo>;</mo><mspace linebreak="newline"/><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#160;</mo><msqrt><msup><mn>313</mn><mn>2</mn></msup><mo>-</mo><msup><mn>312</mn><mn>2</mn></msup></msqrt><mo>.</mo></math></p> <p>&nbsp;</p> <p><strong><span style="text-decoration: underline;"><em>Hướng dẫn giải:</em></span></strong></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>)</mo><mo>&#160;</mo><msqrt><msup><mn>13</mn><mn>2</mn></msup><mo>-</mo><msup><mn>12</mn><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mfenced><mrow><mn>13</mn><mo>-</mo><mn>12</mn></mrow></mfenced><mo>.</mo><mfenced><mrow><mn>13</mn><mo>+</mo><mn>12</mn></mrow></mfenced></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mn>25</mn><mo>.</mo><mn>1</mn></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mn>25</mn></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>5</mn><mo>.</mo></math></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>)</mo><mo>&#160;</mo><msqrt><msup><mn>17</mn><mn>2</mn></msup><mo>-</mo><msup><mn>8</mn><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mfenced><mrow><mn>17</mn><mo>-</mo><mn>8</mn></mrow></mfenced><mfenced><mrow><mn>17</mn><mo>+</mo><mn>8</mn></mrow></mfenced></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mn>25</mn><mo>.</mo><mn>9</mn></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mn>25</mn></msqrt><mo>.</mo><msqrt><mn>9</mn></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>5</mn><mo>.</mo><mn>3</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>15</mn><mo>.</mo></math></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c</mi><mo>)</mo><mo>&#160;</mo><msqrt><msup><mn>117</mn><mn>2</mn></msup><mo>-</mo><msup><mn>108</mn><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mfenced><mrow><mn>117</mn><mo>-</mo><mn>108</mn></mrow></mfenced><mo>.</mo><mfenced><mrow><mn>117</mn><mo>+</mo><mn>108</mn></mrow></mfenced></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mn>9</mn><mo>.</mo><mn>225</mn></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mn>9</mn></msqrt><mo>&#160;</mo><mo>.</mo><msqrt><mn>225</mn></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>3</mn><mo>.</mo><mn>15</mn><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>45</mn><mo>.</mo></math></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#160;</mo><msqrt><msup><mn>313</mn><mn>2</mn></msup><mo>-</mo><msup><mn>312</mn><mn>2</mn></msup></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mfenced><mrow><mn>313</mn><mo>-</mo><mn>312</mn></mrow></mfenced><mo>.</mo><mfenced><mrow><mn>313</mn><mo>+</mo><mn>312</mn></mrow></mfenced></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mn>625</mn><mo>.</mo><mn>1</mn></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><msqrt><mn>625</mn></msqrt><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>25</mn><mo>.</mo></math></p>
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