Question

Đã trả lời bởi chuyên gia

Answer 1

$ \sqrt{12} + 5\sqrt{3} - \sqrt{48} $
\[
\sqrt{12} = 2\sqrt{3}, \quad \sqrt{48} = 4\sqrt{3}.
\]
\[
2\sqrt{3} + 5\sqrt{3} - 4\sqrt{3} = 3\sqrt{3}.
\]
$ 3\sqrt{3} $

$ 5\sqrt{5} + \sqrt{20} - 3\sqrt{45} $
\[
\sqrt{20} = 2\sqrt{5}, \quad \sqrt{45} = 3\sqrt{5}.
\]
\[
5\sqrt{5} + 2\sqrt{5} - 3(3\sqrt{5}) = 5\sqrt{5} + 2\sqrt{5} - 9\sqrt{5} = -2\sqrt{5}.
\]

$ 2\sqrt{32} + 4\sqrt{8} - 5\sqrt{18} $
\[
\sqrt{32} = 4\sqrt{2}, \quad \sqrt{8} = 2\sqrt{2}, \quad \sqrt{18} = 3\sqrt{2}.
\]
\[
2(4\sqrt{2}) + 4(2\sqrt{2}) - 5(3\sqrt{2}) = 8\sqrt{2} + 8\sqrt{2} - 15\sqrt{2} = 1\sqrt{2}.
\]

$ \frac{1}{\sqrt{5}} - 2 + \frac{1}{\sqrt{5}} + 2 $
\[
\frac{1}{\sqrt{5}} + \frac{1}{\sqrt{5}} - 2 + 2 = \frac{2}{\sqrt{5}}.
\]
( \frac{2}{\sqrt{5}} \)

$ \frac{2}{4} - 3\sqrt{2} - \frac{2}{4} + 3\sqrt{2} $
\[
\frac{2}{4} - \frac{2}{4} - 3\sqrt{2} + 3\sqrt{2} = 0.
\]

$ (\sqrt{28} - 2\sqrt{14} + \sqrt{7})\sqrt{7} + 7\sqrt{8} $
\[
\sqrt{28} = 2\sqrt{7}, \quad \sqrt{8} = 2\sqrt{2}.
\]
\[
(2\sqrt{7} - 2\sqrt{14} + \sqrt{7})\sqrt{7} + 7(2\sqrt{2}) = (2 \cdot 7 - 2\sqrt{98} + 7) + 14\sqrt{2}.
\]

$ \sqrt{(\sqrt{5} - 3)^2} + \sqrt{(\sqrt{5} - 2)^2} $
\[
|\sqrt{5} - 3| + |\sqrt{5} - 2| = (3 - \sqrt{5}) + (\sqrt{5} - 2).
\]

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Answer 2

$ \sqrt{12} + 5\sqrt{3} - \sqrt{48} $
\[
\sqrt{12} = 2\sqrt{3}, \quad \sqrt{48} = 4\sqrt{3}.
\]
\[
2\sqrt{3} + 5\sqrt{3} - 4\sqrt{3} = 3\sqrt{3}.
\]
$ 3\sqrt{3} $

$ 5\sqrt{5} + \sqrt{20} - 3\sqrt{45} $
\[
\sqrt{20} = 2\sqrt{5}, \quad \sqrt{45} = 3\sqrt{5}.
\]
\[
5\sqrt{5} + 2\sqrt{5} - 3(3\sqrt{5}) = 5\sqrt{5} + 2\sqrt{5} - 9\sqrt{5} = -2\sqrt{5}.
\]

$ 2\sqrt{32} + 4\sqrt{8} - 5\sqrt{18} $
\[
\sqrt{32} = 4\sqrt{2}, \quad \sqrt{8} = 2\sqrt{2}, \quad \sqrt{18} = 3\sqrt{2}.
\]
\[
2(4\sqrt{2}) + 4(2\sqrt{2}) - 5(3\sqrt{2}) = 8\sqrt{2} + 8\sqrt{2} - 15\sqrt{2} = 1\sqrt{2}.
\]

$ \frac{1}{\sqrt{5}} - 2 + \frac{1}{\sqrt{5}} + 2 $
\[
\frac{1}{\sqrt{5}} + \frac{1}{\sqrt{5}} - 2 + 2 = \frac{2}{\sqrt{5}}.
\]
( \frac{2}{\sqrt{5}} \)

$ \frac{2}{4} - 3\sqrt{2} - \frac{2}{4} + 3\sqrt{2} $
\[
\frac{2}{4} - \frac{2}{4} - 3\sqrt{2} + 3\sqrt{2} = 0.
\]

$ (\sqrt{28} - 2\sqrt{14} + \sqrt{7})\sqrt{7} + 7\sqrt{8} $
\[
\sqrt{28} = 2\sqrt{7}, \quad \sqrt{8} = 2\sqrt{2}.
\]
\[
(2\sqrt{7} - 2\sqrt{14} + \sqrt{7})\sqrt{7} + 7(2\sqrt{2}) = (2 \cdot 7 - 2\sqrt{98} + 7) + 14\sqrt{2}.
\]

$ \sqrt{(\sqrt{5} - 3)^2} + \sqrt{(\sqrt{5} - 2)^2} $
\[
|\sqrt{5} - 3| + |\sqrt{5} - 2| = (3 - \sqrt{5}) + (\sqrt{5} - 2).
\]

Answer 3

câu 1

1:√12 + 5√3 - √48

√12 = √(4*3) = 2√3

√48 = √(16*3) = 4√3

:√12 + 5√3 - √48 = 1/(2√3) + 5√3 - 4√3

5√3 - 4√3 = 1√3 = √3.

1/(2√3) + √3 = 1/(2√3) + (2√3/2)

= (1 + 2*3)/(2√3) = (1 + 6)/(2√3) = 7/(2√3)

7/(2√3) = 7√3/(2*3) = 7√3/6

câu 2

5√5 + √20 - 3√45

√20 = √(4 * 5) = √4 * √5 = 2√5

√45 = √(9 * 5) = √9 * √5 = 3√5

5√5 + √20 - 3√45 = 5√5 + 2√5 - 3 * (3√5)

5√5 + 2√5 - 3 * (3√5) = 5√5 + 2√5 - 9√5

5√5 + 2√5 - 9√5 = (5 + 2 - 9)√5 = -2√5\

câu 3

2√32+4√8-5√18

√32 = √(16 * 2) = √16 * √2 = 4√2

√8 = √(4 * 2) = √4 * √2 = 2√2

√18 = √(9 * 2) = √9 * √2 = 3√2

2√32 + 4√8 - 5√18 = 2(4√2) + 4(2√2) - 5(3√2)

2(4√2) + 4(2√2) - 5(3√2) = 8√2 + 8√2 - 15√2

8√2 + 8√2 - 15√2
= (8 + 8 - 15)√2
= 1√2
= √2

câu 4

1/√5 -2 + 1/√5 + 2

1/(√5 - 2) * (√5 + 2)/(√5 + 2) = (√5 + 2) / ( (√5)² - 2² ) = (√5 + 2) / (5 - 4) = (√5 + 2) / 1 = √5 + 2

1/(√5 + 2) * (√5 - 2)/(√5 - 2) = (√5 - 2) / ( (√5)² - 2² ) = (√5 - 2) / (5 - 4) = (√5 - 2) / 1 = √5 - 2

(√5 + 2) + (√5 - 2) = √5 + 2 + √5 - 2

√5 + 2 + √5 - 2 = 2√5
câu 5

2/4 -3√2 - 2/4 + 3√2

2/(4 - 3√2) * (4 + 3√2)/(4 + 3√2)

= 2(4 + 3√2) / (4² - (3√2)²)

=2(4 + 3√2) / (16 - 18)

= 2(4 + 3√2) / (-2)

= -(4 + 3√2)

= -4 - 3√2

phan số thứ 2

2/(4 + 3√2) * (4 - 3√2)/(4 - 3√2) = 2(4 - 3√2) / (4² - (3√2)²) = 2(4 - 3√2) / (16 - 18) = 2(4 - 3√2) / (-2) = -(4 - 3√2) = -4 + 3√2

(-4 - 3√2) - (-4 + 3√2) = -4 - 3√2 + 4 - 3√2

-4 - 3√2 + 4 - 3√2 = -6√2
câu 6

(√28-2√14+√7)√7 +7√8

√28 = √(4 * 7) = √4 * √7 = 2√7

(2√7 - 2√14 + √7)

(2√7 - 2√14 + √7)√7 = 2√7 * √7 - 2√14 * √7 + √7 * √7

= 2 * 7 - 2√(14 * 7) + 7

= 14 - 2√98 + 7

√98 = √(49 * 2) = √49 * √2 = 7√2

14 - 2 * 7√2 + 7 = 14 - 14√2 + 7 = 21 - 14√2

7√8 = 7√(4 * 2) = 7 * √4 * √2 = 7 * 2 * √2 = 14√2

(21 - 14√2) + 14√2 = 21 - 14√2 + 14√2 = 21

câu 7

√(√5 - 3)² + √(√5 - 2)²

√(√5 - 3)² = |√5 - 3|

√(√5 - 2)² = |√5 - 2|

√5 =2.2

√5 - 3 < 0 => |√5 - 3| = -(√5 - 3) = 3 - √5

√5 - 2 > 0 => |√5 - 2| = √5 - 2

|√5 - 3| + |√5 - 2| = (3 - √5) + (√5 - 2)
= 3 - √5 + √5 - 2
= 3 - 2 = 1

câu 8

4x + √(x - 12) mũ 2 (x ≥ 2)

√(x - 12)² = |x - 12|

Vì x ≥ 2, ta xét hai trường hợp:

Trường hợp 1: 2 ≤ x < 12

x - 12 < 0, do đó |x - 12| = -(x - 12) = 12 - x

4x + (12 - x) = 3x + 12

Trường hợp 2: x ≥ 12

x - 12 ≥ 0, do đó |x - 12| = x - 12.

4x + (x - 12) = 5x - 12

=>
4x + √(x - 12)² (với x ≥ 2) phụ thuoc vào giá trị x

Nếu 2 ≤ x < 12, biểu thức rút gọn bằng 3x + 12

ếu x ≥ 12, biểu thức rút gọn bằng 5x - 12