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Giải bài 2.44 trang 34 sách bài tập toán 7 - Kết nối tri thức với cuộc sống

Không dùng máy tính, hãy cho biết số

𝐆Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên...
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Đề bài

Không dùng máy tính, hãy cho biết số \(\sqrt {\underbrace {11...1}_{101\,chữ\,số\,1}} \) là số hữu tỉ hay vô tỉ. Giải thích.

Phương pháp giải - Xem chi tiết

+) \(\underbrace {11...1}_{101\,chữ\,số\,1}\) có tổng các chữ số bằng 101 +) Số \(\underbrace {11...1}_{101{\kern 1pt} chữ{\kern 1pt} số{\kern 1pt} 1}\) chia 3 dư 2 +) Số \(\underbrace {11...1}_{101{\kern 1pt} chữ{\kern 1pt} số{\kern 1pt} 1}\) không là số chính phương

Lời giải chi tiết

Ta có: \(\underbrace {11...1}_{101\,chữ\,số\,1}\) có tổng các chữ số bằng 101 và 101 chia 3 dư 2 nên số \(\underbrace {11...1}_{101{\kern 1pt} chữ{\kern 1pt} số{\kern 1pt} 1}\) chia 3 dư 2Mặt khác, bình phương của một số tự nhiên chỉ có thể chia hết cho 3 hoặc chia 3 dư 1, do đó số \(\underbrace {11...1}_{101\,chữ\,số\,1}\) không phải là số chính phương.Vì vậy \(\sqrt {\underbrace {11...1}_{101\,chữ\,số\,1}} \) là số vô tỉ.

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