Đáp án+Giải thích các bước giải:
`1)`
`a)\sqrt{(-13)²} = |-13| = 13`
`b) \sqrt{91²} = |91| = 91`
`c) \sqrt{b²} = |b| = -b (b<0)`
`d) \sqrt{9x^4} + 3x²`
`= \sqrt{(3x²)²} + 3x²`
`= |3x²| + 3x²`
`= 3x² + 3x²`
`= 6x² (x²≥0)`
`e) \sqrt{25a²} + 5a`
`= \sqrt{(5a)²} + 5a `
`= |5a| + 5a`
`= -5a + 5a`
`= 0 (a<0)`
`f) \sqrt{(4+\sqrt{7})²}`
`= |4+\sqrt{7}|`
`= 4 + \sqrt{7}`
`g) \sqrt{(2-\sqrt{7})²}`
`= |2-\sqrt{7}|`
`= \sqrt{7} - 2 (2 < \sqrt{7})`
`h) \sqrt{(x-3)²}`
`= |x-3|`
`= x - 3 (x≥3)`
`i) \sqrt{(2x+5)²}`
`= |2x+5|`
`= -2x-5 (x<-2,5)`
`k) \sqrt{x² + 4x + 4}`
`= \sqrt{(x+2)²}`
`= |x+2|`
`= x + 2 (x≥2)`
`l) \sqrt{9x²-18x+9}`
`= \sqrt{(3x)² - 2.3x.3 + 9}`
`= \sqrt{(3x-3)²}`
`= |3x-3|`
`= |3(x-1)|`
`= 3|x-1|`
`= 3(1-x) (x<1)`
`= 3-3x`
`m) \sqrt{8-2\sqrt{7}}`
`= \sqrt{7-2\sqrt{7} +1}`
`= \sqrt{(\sqrt{7}-1)²}`
`= |\sqrt{7} - 1|`
`= \sqrt{7} - 1`
`n) \sqrt{14+6\sqrt{5}}`
`= \sqrt{9 + 6\sqrt{5} + 5}`
`= \sqrt{(3+\sqrt{5})²}`
`= |3+\sqrt{5}|`
`= 3 + \sqrt{5}`
`o) \sqrt{5-2\sqrt{6}}`
`= \sqrt{5 - 2\sqrt{2.3}}`
`= \sqrt{5 - 2 \sqrt{2} . \sqrt{3}}`
`= \sqrt{2 - 2\sqrt{2}\sqrt{3} + 3}`
`= \sqrt{(\sqrt{2}-\sqrt{3})²}`
`= |\sqrt{2} - \sqrt{3}|`
`= \sqrt{3} - \sqrt{2}`
`p) \sqrt{11 + 4\sqrt{7}}`
`= \sqrt{4 + 4\sqrt{7} + 7}`
`= \sqrt{(2+ \sqrt{7})²}`
`= |2+ \sqrt{7}|`
`= 2 + \sqrt{7}`
