Toán Lớp 9: 1)Tính
√(1/5 ×1/20 ×3 ×27)
√[0,001 ×360 ×3^2-(-3)^2]
2)So sánh:
√(4-3√3) và √3 – 1
3)PTĐTTNT
C = √x^3 – √y^3 + √x^2y + √xy^2
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Toán Lớp 9: 1)Tính
√(1/5 ×1/20 ×3 ×27)
√[0,001 ×360 ×3^2-(-3)^2]
2)So sánh:
√(4-3√3) và √3 – 1
3)PTĐTTNT
C = √x^3 – √y^3 + √x^2y + √xy^2
Comments ( 1 )
1)a)\sqrt {\left( {\dfrac{1}{5}.\dfrac{1}{{20}}.3.27} \right)} \\
= \sqrt {\dfrac{{81}}{{100}}} = \dfrac{9}{{10}}\\
b)\sqrt {0,{{001.360.3}^2}} – {\left( { – 3} \right)^2}\\
= \sqrt {0,{{01.36.3}^2}} – 9\\
= 0,1.6.3 – 9\\
= 1,8 – 9\\
= – 7,2\\
2)\sqrt {4 – 3\sqrt 3 } < \sqrt {4 – 2\sqrt 3 } \\
DO:\sqrt {4 – 2\sqrt 3 } = \sqrt {{{\left( {\sqrt 3 – 1} \right)}^2}} = \sqrt 3 – 1\\
\Leftrightarrow \sqrt {4 – 3\sqrt 3 } < \sqrt 3 – 1\\
3)C = \sqrt {{x^3}} – \sqrt {{y^3}} + \sqrt {{x^2}y} – \sqrt {x{y^2}} \\
= \left( {\sqrt x – \sqrt y } \right)\left( {x + \sqrt {xy} + y} \right) + \sqrt {xy} \left( {\sqrt x – \sqrt y } \right)\\
= \left( {\sqrt x – \sqrt y } \right)\left( {x + \sqrt {xy} + y + \sqrt {xy} } \right)\\
= \left( {\sqrt x – \sqrt y } \right)\left( {x + 2\sqrt {xy} + y} \right)\\
= \left( {\sqrt x – \sqrt y } \right){\left( {\sqrt x + \sqrt y } \right)^2}
\end{array}$