Mathematics
BrandeVenturella
27

simplify each square root: 1. square root of -25 2. square root of 1.44 3. square root of + or -16/49 4. square root of 361 5. square root of 49 6. square root of + or -0.64 7. square root of -6.25 8. square root of 169/196 9. square root of 25/324

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(1) Answers
Nunia1567

[latex]1.\ \sqrt{-25}-isn't\ real\ number\to\sqrt{-25}=\sqrt{25(-1)}=\sqrt{25}\cdot\sqrt{-1}=5i\\\\2.\ \sqrt{1.44}=\sqrt{1.2^2}=1.2\\\\3.\ \sqrt{\frac{16}{49}}=\frac{\sqrt{16}}{\sqrt{49}}=\frac{\sqrt{4^2}}{\sqrt{7^2}}=\frac{4}{7}\\\\\sqrt{-\frac{16}{49}}=\frac{4}{7}i\\\\4.\ \sqrt{361}=\sqrt{19^2}=19\\\\5.\ \sqrt{49}=\sqrt{7^2}=7\\\\6.\ \sqrt{0.64}=\sqrt{0.8^2}=0.8\\\\\sqrt{-0.64}=0.8i[/latex] [latex]7.\ \sqrt{-6.25}=\sqrt{6.25(-1)}=\sqrt{6.25}\cdot\sqrt{-1}=\sqrt{2.5^2}\cdot\sqty{-1}=2.5i\\\\8.\ \sqrt\frac{169}{196}=\frac{\sqrt{169}}{\sqrt{196}}=\frac{\sqrt{13^2}}{\sqrt{14^2}}=\frac{13}{14}\\\\9.\ \sqrt\frac{25}{324}=\frac{\sqrt{25}}{\sqrt{324}}=\frac{\sqrt{5^2}}{\sqrt{18^2}}=\frac{5}{18}\\====================================[/latex] [latex]i=\sqrt{-1}\ is\ the\ imaginary\ unit\\---------------------\\If\ a\geq0\ then\ \sqrt{a^2}=a[/latex]

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