Bài 29. Tính
a) \( \frac{\sqrt{2}}{\sqrt{14}}\); b) \( \frac{\sqrt{15}}{\sqrt{735}}\);
c) \( \frac{\sqrt{12500}}{\sqrt{500}}\); d) \( \frac{\sqrt{6^{5}}}{\sqrt{2^{3}.3^{5}}}\).
Hướng dẫn giải:
Áp dụng quy tắc chia hai căn thức bậc hai.
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Ta có:
a) \(\frac{\sqrt{2}}{\sqrt{18}}=\sqrt{\frac{2}{18}}=\sqrt{\frac{1}{9}}=\frac{1}{3}\)
b) \(\frac{\sqrt{15}}{\sqrt{735}}=\sqrt{\frac{15}{735}}=\sqrt{\frac{1}{49}}=\frac{1}{7}\)
c) \(\frac{\sqrt{12500}}{\sqrt{500}}=\sqrt{\frac{12500}{500}}=\sqrt{25}=5\)
d) \(\frac{\sqrt{6^{5}}}{\sqrt{2^{3}.3^{5}}}=\sqrt{\frac{6^5}{2^3.3^5}}=\sqrt{\frac{2^5.3^5}{2^3.3^5}}=\sqrt{2^2}=2\)