Giải bài 2 trang 56 vở thực hành Toán 9

Thực hiện phép tính: a) (sqrt 3 left( {sqrt {192} - sqrt {75} } right)); b) (frac{{ - 3sqrt {18} + 5sqrt {50} - sqrt {128} }}{{7sqrt 2 }}).

Tổng hợp Đề thi vào 10 có đáp án và lời giải

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Đề bài

Thực hiện phép tính: a) \(\sqrt 3 \left( {\sqrt {192} - \sqrt {75} } \right)\); b) \(\frac{{ - 3\sqrt {18} + 5\sqrt {50} - \sqrt {128} }}{{7\sqrt 2 }}\).

Phương pháp giải - Xem chi tiết

a) + \(\sqrt {{a^2}} = \left| a \right|\) với mọi số thực a. + Với A, B là các biểu thức không âm, ta có \(\sqrt A .\sqrt B = \sqrt {AB} \). b) + \(\sqrt {{a^2}} = \left| a \right|\) với mọi số thực a. + Nếu A, B là các biểu thức với \(A \ge 0,B > 0\) thì \(\frac{{\sqrt A }}{{\sqrt B }} = \sqrt {\frac{A}{B}} \).

Lời giải chi tiết

a) \(\sqrt 3 \left( {\sqrt {192} - \sqrt {75} } \right) = \sqrt 3 .\sqrt {192} - \sqrt 3 .\sqrt {75} \) \(= \sqrt {3.192} - \sqrt {3.75} = \sqrt {{{3.3.8}^2}} - \sqrt {{{3.3.5}^2}} \) \(= 3.8 - 3.5 = 9\) b) \(\frac{{ - 3\sqrt {18} + 5\sqrt {50} - \sqrt {128} }}{{7\sqrt 2 }} \) \(= \frac{{ - 3\sqrt {18} }}{{7\sqrt 2 }} + \frac{{5\sqrt {50} }}{{7\sqrt 2 }} + \frac{{ - \sqrt {128} }}{{7\sqrt 2 }}\) \( = - \frac{3}{7}\sqrt {\frac{{18}}{2}} + \frac{5}{7}\sqrt {\frac{{50}}{2}} + \frac{{ - 1}}{7}\sqrt {\frac{{128}}{2}} \) \(= - \frac{3}{7}\sqrt 9 + \frac{5}{7}\sqrt {25} + \frac{{ - 1}}{7}\sqrt {64} \) \( = - \frac{3}{7}.3 + \frac{5}{7}.5 + \frac{{ - 1}}{7}.8 = \frac{8}{7}\)

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3.7 trên 3 phiếu

෴ Giải bài 3 trang 56 vở thực hành Toán 9 Chứng minh rằng: a) ({left( {1 - sqrt 2 } right)^2} = 3 - 2sqrt 2 ); b) ({left( {sqrt 3 + sqrt 2 } right)^2} = 5 + 2sqrt 6 ).
✨ Giải bài 4 trang 56 vở thực hành Toán 9 Cho căn thức (sqrt {{x^2} - 4x + 4} ). a) Hãy chứng tỏ căn thức xác định với mọi giá trị của x. b) Rút gọn căn thức đã cho với (x ge 2). c) Chứng tỏ rằng với mọi (x ge 2), biểu thức (sqrt {x - sqrt {{x^2} - 4x + 4} } ) có giá trị không đổi.
𝕴 Giải bài 5 trang 57 vở thực hành Toán 9 Vận tốc (m/s) của một vật đang bay được cho bởi công thức (v = sqrt {frac{{2E}}{m}} ), trong đó E là động năng của vật (tính bằng Joule, kí hiệu là J) và m (kg) là khối lượng của vật (Theo Vật lí đại cương, NXB Giáo dục Việt Nam, 2016). Tính vận tốc bay của một vật khi biết vật đó có khối lượng 2,5kg và động năng 281,25J.
෴ Giải bài 6 trang 57 vở thực hành Toán 9 Vận tốc của ô tô và vết trượt bánh xe trên mặt đường khi xe phanh gấp liên hệ với nhau bởi công thức ({v^2} = 20kl), trong đó v(m/s) là vận tốc của xe khi phanh gấp, k là hệ số ma sát giữa bánh xe và mặt đường khi xe phanh và l(m) là độ dài vết trượt của bánh xe trên mặt đường. a) Viết công thức tính vận tốc xe theo hệ số ma sát k và độ dài l của vết trượt bánh xe khi ô tô phanh. b) Ô tô đang chạy trên mặt đường thì phanh gấp và tạo ra vết trượt của bánh xe dài 25m. Biết hệ số ma sát giữa bá
𒐪 Giải bài 7 trang 57 vở thực hành Toán 9 Không dùng MTCT, tính giá trị biểu thức sau: (A = frac{{sqrt 2 + sqrt 3 + sqrt 6 + sqrt 8 + sqrt {16} }}{{sqrt 1 + sqrt 2 }} - left( {sqrt 1 + sqrt 2 + sqrt 3 + sqrt 4 } right)).

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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